I sent a short story to a magazine a week or so ago, and was wondering how long these things normally take come back?

I'm such an impatient person, and I find it hard to get on with other things whilst waiting, which is really daft, as I'm just wasting time really.

Also, when it comes to submissions, what goes on the cover letter? I always try to keep it as short as possible, and let the story speak for itself. Should it be more meaty?

The magazine submission guidelines normally tell you how long each magazine will take to respond. If not, then it's best to make a quick phone call before sending the work out, so you can make a note of when to start chasing them. A week is a very short time in magazine terms.... you might have to get used to being more patient. For instance, some poetry/short story mags will say three months for a response, due to the huge number they receive.

Regarding covering letters, they're your selling tool, so they shouldn't be too verbose. You need to give a flavour of the story/piece, mention any previous successes you've had in terms of selling your work, make it clear what part of the magazine your work is intended for and then let the work speak for itself. This is true of practically all covering letters anyway. Good luck.

No, here you are talking 4 months. Usually, as Anna has said, if you read their literature you can get an idea of how long they, on average, take to respond.
If you haven't already, set yourself out some form of keeping track. I use two. One tells me all the info I need about the publisher, format, payment or not, preferred genre, multiple or simultaneous subs, expected response time, etc. The other tells me where I have sent the work, how I sent it,(snail or email), when I should hear back, that sort of thing. some mags, especially those who take email subs can be swamped with as many as 4 thousand pieces of work. They ditch the crap quickly enough after reading the first one or two paras, get to the possibles, and then deliberate, sometimes for a while on the good work.
If you send a cover, be as brief as possible, if they don't ask for a writing history, don't send one, but you could say you can give them one if they want it. Three lines max. Good luck
Becca.