Bridge is all about counting the cards, and this article aims to give an introduction to the basics, then to discuss the matter a little more deeply.
Standard count refers to the way you follow suit. Many people play that a high card followed by a low card (a peter) shows an even number of cards in that suit. It doesn't tell you whether he has two or four, but it does tell you he hasn't three, and that may be vital to the defence.
Whilst most people are familiar with following suit to show count, it can also be applied when returning a suit. If you have A95 in the suit, win the ace, then play the nine to show an even number left, or with A952, return the 2 to show an odd number of cards left in the suit. (Strangely enough, with A9542 it is standard to return the 4, though the theoretical basis for this has always eluded me.)
Similarly, standard leads are to play fourth highest from an honour, and second highest from a weak suit (no honour card - the ten you can treat as an honour or not depending on your mood!). Thus with 984 you would lead the eight, and then play the nine to show an even number left, or with 9842, the eight and then the two to show an odd number left. Technically you might like to take this last suit to the extreme case, playing the eight as second highest lead, then the 2 to show an odd number left, then the nine to show an even number left, and finally the 4. If partner hasn't worked out your count by this time, he never will! (And for this reason, many people would use the 9 and the 4 for suit preference purposes - but that will have to wait until another article.)
Which cards to play: We described count signals slightly incorrectly - more accurate would be to say that playing a higher card shows an even number left, and a lower card an odd number left. There are two points I am making here: (a) There are no high and low cards - it depends what your holding is. For example, with 432 the 4 is a higher card, whilst with 1098, the eight is a lower card. (b) The aim is for the first card to tell partner the count - not for him to have to wait for the second. This is important partly because it is often vital to need to know the count straight away, but also to make life easy for partner. If you have 9632 don't play the three, knowing that you can follow up with the 2; play the nine or six to make it more clear.
This brings us onto an important point. Generally to show count you should play the highest or lowest that you can afford. However, with four cards there are two theories. Some people like to play the highest that they can afford, whilst others prefer to always play the second highest, on the basis that you often cannot afford the highest, so it is better to be consistent about it. (And with some partners I play second highest unless the top two are touching, when we play the highest if it is a ten or above.) However, a vital part of this is that you can afford it - with J932 you may well have to play the three. (Though note that with J632 you would play the six.) With doubletons, you should play the high card if it is a jack or below, but not with the queen. Again sometimes you should exercise discretion with a jack too, whilst you should never play the queen as this indicates either the jack or a singleton.
Combining count and attitude: This is not the place for a discussion of attitude signals, but generally if you play attitude instead of count, where a high card shows that you like the suit, you should use the same principles as you did for count. In addition, when making subsequent plays in the suit they should still be count signals. Thus with 9832, and playing attitude signals, you should follow to partner's ace with the two, and then follow up with the three to show an odd number of cards left. Do not play the three first, hoping to discourage, and then follow with the two later to give the count, as this shows that you like the suit!
Count and attitude (or reversed if you fancy) are the two almost universal ways of following suit. Attitude tends to be preferred more by top partnerships, whilst count is much easier to play, and preferred by many for simplicity (it is easy to count the number of cards you have in a suit!). Ideally, a combination should be used, but that makes life even trickier. But don't try to give both at once - signals can be hard enough to read as it is, without trying to convey your whole hand with some incredibly refined methods!