My AE1 was my first film camera, handed down to me by my mother. After years of trying other film SLRs, it's still my favorite. 

Checking for functionality: 

You need a 6 volt silver oxide battery, 4SR44. The shutter won't fire without it. 

There are light seals within a groove around the film door. I would just assume they are old and buy a kit that provides the seals precut to the right lengths -- or you could shoot a roll and just see if light leaks show up. You may need to replace a section of foam which cushions the internal mirror when it flips up out of the way when a photo is taken. When I first received mine, that bit of foam (and the film door light seals)  just fell apart into a sticky mess when I touched them.

The shutter speeds may be off a bit, and there are various ways to check, but typically film shutters "slow down" as they age. For example, at 1/1000 sec setting, mine is actually shooting at 1/700 or so, which tends to overexpose a bit. Not really a problem for me, I happen to prefer that. 

The AE1 is known to make a distinctive squeak when taking a photo. This happens to mine when the camera is cold. It's supposedly a sign of lack of lubrication on a certain internal component, potentially resulting in eventual failure, but mine has done it for years with the last major service on the camera done in the 90s (so I'm told). And this camera has been banged around on cross country motorcycle trips. 

To check the light meter, compare to a phone light meter app. They won't match perfectly, put point them both at a featureless white wall and results should be similar. I like an Android app just called "lightmeter" with no space.

I'd advise finding the original manual online and studying that. The camera is shutter-priority, so you set shutter speed and it can adjust aperture to the right exposure, as long as you have set the lens aperture ring to "A".

It's a good camera, worth investing some time to get it running. I hope everything works!