Prefnote
First become familiar with the very basic concepts of consulting the Yi Jing before reading this simple survey. You should aready know at least one method of casting a hexagram and the meaning of terms such as "trigram," "changing line," and "static line." Nothing here is original -- all credits go to the original authors; and apologies for any misrepresentations.

1. Turtle shell / ox bone
Crack a turtle shell with heated rocks or sticks.   Read the pattern of the cracks.^I

2. Yarrow (milfoil plant) sticks
Along with shell and bone cracking, the manipulation of a group of yarrow stalks is the oldest method of consulting the oracle. The procedures in use today are complex and time-consuming^II; but they do serve to focus and clear the questioner's mind. This is an example of how the yarrow method can work:

Repeat five times to determine the remaining five lines of the hexagram. Multiple changing lines are possible (more so than with the yarrow stick method). Some schools provide systems for limiting the number of changing lines recognized when using the yarrow and three-coin methods.^V

4. Four coins
The tossing of 3 coins and the dividing of yarrow stalks do not have the same statistical probabilities in producing lines. In the belief that the yarrow method is more reliable and/or more ancient, some 4-coin methods have been developed that duplicate the probabilities of yarrow divination.[VI]  For example:

6. Six coins [Sorrell/Sorrell]
Toss 5 pennies and 1 dime with eyes closed. (Six pennies, one of which is visually different, would also be acceptable.) Use hands to form coins into a column representing the hexagram. Open eyes and read:

7. Six sticks
Six four-sided sticks are used. Yin and yang lines -- static and changing -- are marked on the four faces of each stick. The distribution of the line markings varies. Sometimes each stick is marked with all four types of lines. Cast the sticks and form them into the shape of a hexagram. Even more that the 3-coin method, this increases the probability of receiving changing lines.^VII

8. Sixty-four sticks
Place 64 numbered bamboo slips into a wooden or bamboo cup. Shake the cup until one or two slips slip out. Read the corresponding hexagram(s).^IX

9. Yarn sticks
Pick a group of yarn sticks at random from a container of less than 50 sticks. This determines your lower trigram. Repeat the process for the upper trigram. There are no changing lines.^X

11. Six questions [Lofting]
The inquirer is asked two sets of three questions about his inquiry. Based on the answers, a hexagram is built. The first three questions deal with the inquirer’s ("my") assessment of the situation:

12. Gender method [Perrottet]
In The Visual I Ching,^XIIthe inquirer takes eight cards, each displaying a visual image of a trigram, and holds them or places them face-down. He then mixes them up, chooses one, and notes it. This is repeated five more times. Trigrams associated with male members of the family yield yang lines, and vice versa:

13. Eight gems and a die [A. Huang]
Place eight different stones into a bag (predetermining which stones represent each of the 8 trigrams). Pick a stone; this is your lower trigam. Place it back in the bag. Pick a stone; this is your upper trigram. Roll the die. The number on the die is the number of the hexagram's changing line.^XIII

14. Sixteen cards and a die [A. Huang]
On 8 red cards and 8 blue cards mark the symbols of the 8 trigrams. Shuffle the cards upside down and choose one blue card for the lower trigram and one red card for the upper trigram. Roll a die to determine the number of the changing line.

15. Cassia Tora seeds. [Ni]
Six "pinches" of small seeds or grains of rice are placed on a plain sheet of paper, representing the 6 lines of a hexagram. If a cluster of seeds contains an even number of seeds, the line is yin; if odd, yang. One additional pinch of seeds is dropped and counted. This determines which line is the one on which to focus. If the number is greater than 6, 6 is subtracted and the remainder is the focus line. ("Focus line" is my term to indicate no additional hexagram is to be consulted.)^XIV

16. Situation-related trigrams [Shao Yong, c. 1066]
In this method, aspects of a particular situation are used to determine the trigrams which relate to it. The relationships of the trigrams' imagery are then examined to determine a reading.^XV  "Aspects" include such things as:

18. And finally, just open the book at random and read it.
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Footnotes:

I   A small hole is drilled on one side of the shell.  The heat source is applied there and the cracks form on the other side.  One "cracking" requires approximately 1.5 square inches of shell.  This method was used with turtle shells and with bones -- usually the shoulder blades -- of oxen.

II   The methods in use today are from 1,000 to 3,000 years old.  The exact date is a subject of much scholarly debate.  Most methods today are based on a description in a collection of Confucian-style commentaries on the Yi Jing known as the Ten Wings (in particular, see Chapter 9 of the Great Treatise/Appended Judements of the Ten Wings).   The language in all the Ten Wings is full of imagery.  Here is just one passage about the yarrows:

The number of the Great Expansion is fifty,
Of which forty-nine are used.
Divide them into two, symbolizing the two primary forces.
Suspend one, symbolizing the three supreme powers.
Manipulate by four, symbolizing the four seasons.
Return the remainder, symbolizing the intercalary month.
In five years there is another intercalation.
Afterward the process is repeated.

Therefore four operations produce a change,
And eighteen changes yield a gua.    (--Translation A. Huang)

III   Here is the basic chart when counting "leftovers:"

27 = An "old" (changing)  yin (broken) line
21 = A "young" (static) yang (solid) line
17 = A young yin line
13 = An old yang line

IV   Diana ffarington Hook's The I Ching and You  (0-7100-7381) includes one description of the symbolism involved in the 3-coin method.  (Thanks to Isabeau Vollhardt for the quotation):

...where there is a mixture of heads and tails, that is 7 or 8 in a single throw, there is a more or less balanced condition, part yang and part yin, and the answer is a yang or yin line. However, when all three coins fall the same way up, that is three heads (9) or three tails (6), the situation is unbalanced, being either too yang, or too yin. These lines are then in an important state of change or movement, changing because of the excessive imbalance.

VI   There are multiple methods that use four coins and exactly duplicate the probabilities of using yarrow stalks.  Edward Hacker presents his in his book The I Ching Handbook (ISBN 0-912111-36-4).  Stuart Anderson, whose description of "Alternate Coin Method #2" appears above, has laid out the mathematics (along with another 4-coin method) in his article at Charlie Higgins YJ Mensionization site http://www.mension.com/probab1.htm .  A third 4-coin method was mentioned by Al Franken.  In this method, four coins are tossed at once; however two of these are pre-designated to work together and count as only one coin.  Again, "heads" = 3, and "tails" = 2.  However, if either of the predesignated pair is a "heads," they both count as one "heads."  The resulting hexagram lines are then the same as in the 3-coin method where 6 = changing yin, etc.  Al Franken pointed out he prefers a 'statistically correct' 4-coin method because hexagrams obtained by yarrow or 4-coin methods are less pessimistic than those of the traditional 3-coin method.  Ralph Abraham ( http://www.ralph-abraham.org/  ) demonstrates mathematically why yarrow probabilities are more "optimistic" than those of the coin oracle:
 

[In regard to the probabilities of obtaining a particular type of line using the yarrow method:]  All this is explained in detail in Wilhelm, pp. 721-722. In summary:

6            -x-                  old yin                             1/16
7            ---                  young yang                      5/16
8            - -                  young yin                          7/16
9            -o-                  old yang                           3/16

This is radically different from the coin oracle, and this is just one reason for preferring the yarrow method.

In practice, an experienced hand will not achieve these  probabilities, for the reason described above. In avoiding the  very unequal divisions, a small advantage is gained to the  remainder 8 and its score 2, and so the expectation of a 6 line,  old yin, will be a bit larger than 1/16. This effect is included in  our simulation by the use of a chaotic attractor to arrange the  heap. By a series of experiments, you may choose a heap  algorithm to match your own hand.

Line probabilities in the first hexagram
Casting a hyperhexagram with 18 divisions of yarrow  determines two hexagrams. A yang line in the first hexagram  results from either a young yang or an old yang hyperline in the  hyperhexagram. Thus the probability of an initial yang line is  the sum of the probabilities of old yang (3/16) and young yang  (5/16) or 8/16: 50%.

 The chances of an initial yin line are similarly the sum of old yin  (1/16) plus young yin (7/16), or 8/16: 50%. Initially, yang and  yin are equiprobable. This is the same as the coin oracle, in  which initial yin and yang are also balanced 50-50.

Probabilities for changing lines
The chances of a changing yarrow hyperline are (1/16) for old  yin, plus (3/16) for old yang, or 4/16: 25%. Again, this is the  same as in the coin oracle.

Line probabilities in the second hexagram
In the second hexagram, a yin line results from either an  original young yin (7/16) or an old yang (3/16) or 10/16 = 5/8.  Similarly, a yang line results from either an initial young yang  (5/16) or an old yin (1/16) pr 6/16 = 3/8. Here we have a  significant difference between the yarrow-stalk oracle and the  coin oracle.

With the YSO, final yin is 5/3 times more likely than yang.  This is the reason for thinking that the coin oracle has  contributed to world problems.

In each coin toss there is one chance in two or probability of  1/2 of obtaining a head or a tail. As three coin tosses determine  a line, it is easy to compute the probabilities of the four lines:

6         -x-               old yin                           1/8
7         ---               young yang                  3/8
8         - -               young yin                      3/8
9         -o-               old yang                       1/8

After casting a hyperhexagram with six tosses of three coins, a  yang line in the first hexagram results from either a young yang  or an old yang hyperline. Thus the probability of a yang line is  the sum of the probabilities of old yang (1/8) and young yang  (3/8) or 4/8, 50%. The chances of a yin line are likewise 50%.  This is an equal opportunity system.

The chances that a hyperline will be changing, old yang or old  yin, is (1/4 + 1/4) or 25%.

VII   Roderic Sorrell and Amy Max Sorrell's I Ching Made Easy (ISBN 0-06-251073-8) is an accessible, good introduction to the Yi Jing.  They also have a website at:  http://www.teleport.com/~bioching/iching.html

VIII   Hacker describes two similar methods using 6 or 12 flat "wands."  Same idea; flatter sticks.  (See Chapter 10 in Hacker.)

IX   For example, see Zhao Xiamin & Martin Palmer's Chinese Fortune Stalks (ISBN 1-55670-985-4).

X   Based on Evelyn Lip's Chinese Numbers (ISBN 0-89346-376-0).

XI   See Chris Lofting's Book of Changes (IC+) at:  www.ozemail.com.au/~ddiamond/index1.html

XII   ISBN 0-8048-3102-5.  Visual I Ching also includes a set of 64 cards, each representing one of the hexagrams.  A "pick one" method suggests itself.

XIII   For more details, see Alfred Huang's The Complete I Ching (ISBN 0-89281-656-2)

XIV   See pp. 208-211 of Ni's I Ching (ISBN: 0937064815).  http://taostar.com/

XV   See http://www.netowne.com/eastern/iching/ for a good brief overview.  This provides just a sample of the master mathematician's methods in the Meihua Xinyi (Plum Flower Mind Yi Jing)  There is no full English translation of that work available as yet.