Entire books exist on this topic; this is just a brief summary. At the end, you will get to practice with 4 deals.
Shown here are "Standard" (in the U.S.) signals.
The 3 main types of signals are shown here. By far, the most important is the "Attitude Signal." We'll leave that to last and look at the other two first:
1) Count Signal
This is used when declarer leads the suit (either from his hand or from dummy). To show an even number of cards, play hi-lo. To show an odd number of cards, play lo-hi.
For example, the K is led from dummy and you have 92. Play the 9 to show partner you started with 2 or 4 (or 6) spades. With 1092, play the 2 to show you started with 1 or 3 or 5 cards,
2) Suit preference signal
This is used when actually leading a suit in the middle of the hand. Here are the 2 most common uses:
a) When giving a ruff: Partner leads a singleton and you have AK82 in the suit. After taking the king and ace, you give him a ruff. But, do you play the 8 or the 2 for him to ruff? If you play the 8, you are saying "Partner, after you trump this, please come back to me in the highest ranking remaining suit." If you play the 2, you are saying "Partner, after you trump this, please come back to me in the lowest ranking remaining suit." The trump suit and the suit you play are not considered. There are always 2 other suits. So, if they are in 4 and you have AK82, returning the 8 would suggest diamonds and the 2 would suggest clubs.
b) When clearing your suit against notrump, to let partner know how to reach you.
Against 3NT, you lead the 4 from K9842. Dummy has Jxx. Luckily for you, partner wins the A, returns the 3 and you win the king and clear the suit (declarer started with Q10x). But, with which spade do you clear the suit? With a suit-preference card. The 2 would show an entry/desire for the low suit. The 9 for the high suit. Here, you even could ask for the middle suit if partner is carefully watching the spots.
3) Attitude Signal
This is by far the most important signal. It is used in two very important situations:
a) Partner leads to the trick. If partner or dummy is winning the trick, tell partner your attitude. Play a high spot card if you like it, low if you don't. For example, partner leads a spade and dummy's ace takes the trick. Play the 8 if you have KQ82. Play the 3 if you have 843.
b) You make your first discard. Throw the 9 if you like/want hearts; throw the 3 if you don't like hearts.
Do not make attitude signals with cards above the 10. Don't signal with what could potentially be a trick. Of course, you won't always be dealt the right card to signal with.
Note: There are many possible variations to what is shown here. There are many methods I like (such as odd-even) or upside-down. This is just intended as a mainstream summary.
Here are 4 practice deals:
1 No Entry
2 Multiple Signals
3 Partner's Aren't Perfect
4 Subtle or Over the Head?
For more practice deals, click here, and then download the demo (under the picture of the CD).