Three coins

This is probably the better known and most commonly used method to get a response from the I Ching.

Chinese coins of the type also used for Feng Shui (as the ones in the picture) may help in getting the right mood but it is not essential: any coin will do. Ideally they should be identical but, again, this is not relevant. What is important is that you can distinguish the two sides of each coin.
To cast an hexagram you will proceed as follows:

1. Assign 2 to one side of each coin and 3 to the other one.
2. Throw the three coins, sum the face values and draw the resulting line according the following table:
   

   6	7	8	9

3. Repeat step 2 other five times drawing the resulting lines from the bottom to the top of the hexagram.

There is no rule for when one of the coins falls off the table, or it is impossible to determine which side the coin fell (e.g. because it ended up under a piece of furniture). It's up to you to decide what to do in those cases.

This method is known to exist at least since the 7th century CE [1] or even a couple of centuries before [2]; it was popular during the T'ang dinasty. It's very easy and uses common objects that are easy to carry, no wonder it is still in so widespread use today.

Some criticized the usage of coins on the basis that the "true" method is the one using 50 yarrow stalks. Actually, this argument does not hold much as the original yarrows stalks method, which were in use around the year 200BC, is lost and what we have today is a reconstruction that dates around the year 1200CE [2].
Saying that using yarrow stalks (the way we know how to use them) is "truer" than using the coins has no much historical basis.

Others point out that since the assignment of the values to the faces is completely arbitrary, you could get the opposite hexagram instead of the "right" one. Personally I'm not so much worried about being "right" but I feel a little bit uneasy about the arbitrariety of the aassignement of values to faces. Actually this was one of the main reason for starting my search for an alternative casting methods that I felt more comfortable with.

If you prefer using chinese coins, as the ones in the picture, the side with four ideograms is usually considered 3. You can easily buy them online for a rather cheap price.

Probabilities

If we just consider the face that each coin can show after each throw, there are eight possible outcome:

2+2+2 = 6
2+2+3 = 7
2+3+2 = 7
3+2+2 = 7
2+3+3 = 8
3+2+3 = 8
3+3+2 = 8
3+3+3 = 9

Meaning that:

Prob(6) = Prob(9) = ¹/₈ = 12.5%
Prob(8) = Prob(7) = ³/₈ = 37.5%
Prob(yin) = Prob(yang) = ¹/₂

This implies that the probability for a line to be a moving line is ¹/₄ , exatly as for the yarrow stalks method but getting a moving yin line will be as frequent as getting a moving yang line.

References

[1] Lars Bo Christensen, I Ching - The Original Core of the Book of Changes, 2015, http://zhouyi.dk/
[2] Shih Chuan Chen, How to form a hexagram and consult the I Ching, in Journal of the American Oriental Society, 92.2 (1975), http://www.biroco.com/yijing/Shih-chuan_Chen.pdf
[3] How to consult the Yijing, http://www.biroco.com/yijing/basics.htm

Coins image: https://commons.wikimedia.org/wiki/File:Ichingcoins.JPG