I was recently revising the English-French entry for the word who and felt that, in addition to the dictionary entry, some words of explanation may help. Who is one of those awkward little words that feels like it should be simple, but sometimes things aren't that straightforward. It's also a frequently searched-for word in the dictionary.
Who when used to ask a question
When used to ask a question, the French word for who is practically always qui. But as with asking questions in French generally, what happens to the rest of the sentence can be more tricky.
In informal speech, a very common way to ask a question is to use what's technically called an in situ question. This is a question with "normal sentence order". In English, in situ questions are generally only used for emphasis or to suggest surprise ("you saw who yesterday?"). But in French, at least in informal speech, they're a common, neutral way of asking a question:
(1) T'as vu qui?
Literally: "You've seen who?"
Who did you see?
Vous voyez qui ce soir?
Literally: "You are-seeing who this evening"
Who are you seeing this evening?
(2) Elle vient avec qui?
Literally: "She comes with who?"
Who's she coming with?
(3) Qui est là?
Qui vient demain?
Who's coming tomorrow?
When qui is the subject of the verb, as in the last example, the verb generally takes the il/elle (3rd person singular) form. As in English, a common exception is qui sont...? for who are...?. Notice too that the abbreviated form t'as is common in this informal style, whereas in more formal/careful speech and writing, the form would be tu as. To give you an idea of level of formality, (1) and (2) would be acceptable when talking with or writing an e-mail to a friend (or in an on-line chat session). (3) is pretty much always acceptable: when qui is the subject, there's really no other place in the sentence to move it to...!
Qui can also be used with est-ce que, often used as a general "question marker" in French. However, as the subject, the form is qui est-ce qui. (If you're not familiar with the notions of subject and object, then roughly speaking, qui is the subject when it is asking about who is doing the action, and the object when asking about who is receiving it; another way of looking at things is that it's probably the subject if there isn't some other subject!) Here are some example sentences with qui est-ce que and qui est-ce qui:
Qui est-ce qui vient?
Qui est-ce que tu as vu hier?
Who did you see yeterday?
Avec qui est-ce qu'il vient?
Who is he coming with?
These forms are not particularly informal or formal: they would generally be acceptable in most spoken and written contexts. Notice how in French, you would never split up avec qui, whereas in English, it sounds quite unnatural not to use the formula who ... with?.
In formal French, if qui is the object of the verb (or of a preposition), then it can be used with inversion: qui invitez-vous?; avec qui vient-il?. When inversion is acceptable, which form is used and how formal it sounds is quite a complex issue. At GCSE/SAT level, try and make sure you understand inversion, but you'll generally not need to use it.
Who in relative clauses
Something that occurs in various languages is that the words used to ask questions are also used to introduce relative clauses: in other words, a description that is a "sentence inside a sentence", as in the man who I saw yesterday.
In these cases, French uses qui for the subject and que for the object. For example:
L'ami qui vient demain...
The friend who's coming tomorrow...
L'homme qui m'a aidé.
The man who helped me.
(qui is the subject of 'vient'/'aider')
L'ami que je vois ce soir...
The friend who I'm seeing tonight...
L'homme que j'ai vu hier.
The man who I saw yesterday.
(que is the object of 'vois'/'ai vu': notice how there's another subject, je, as a clue that qui/que can't be the subject in this case)
However, qui is still used for the object of a preposition:
L'ami avec qui je sors ce soir.
The friend who I'm going out with tonight.
Notice that in standard French, avec qui is not split up, whereas in English the usual formula is to split up who ... with. Some French speakers might actually sometimes say "...que je sors avec", but this is definitely non-standard, would be consider "uneducated" by many speakers, and would be avoided in more careful speech and writing. For more details about this construction, see Ball, R. (2000) referenced below.
 A more formal definition is that the subject is the part of the sentence that the verb "agrees" with.
For an overview of the standard question forms with qui, see Price (2007), A Comprehensive French Grammar, pages 194 onwards.
For information about various non-standard question forms and relative clauses that occur in colloquial speech, I recommend Ball, R. (2000), Colloquial French Grammar. See pages 26-55.