Generally speaking, older camera bodies were made of metal and tend to withstand much more abuse than their modern (mostly plastic) equivalents. Older lenses, however, have coatings which are often softer than modern ones, and caution needs to be exercised so as not to scratch them.

The Canon AT-1, however, is a derivative of the Canon AE-1, which has a plastic top plate despite its metally looks. I would try to avoid using strong solvents like isopropyl alcohol or naphtha (lighter fluid) that are usually recommended for cleaning metal bodies. The wet wipes they sell for the purpose of cleaning smartphones and displays should be a good option. You can use these to clean the outside of the lens housing, too (though not the lens surfaces, see below). For extremely stubborn stains, try a small amount of alcohol on a cotton bud; for corrosion, a small amount of vinegar. (Anecdotal evidence: I have used naphtha and vinegar on the bodies of Minolta XD series cameras, which I believe have a similar metallized plastic top plate, to no ill effect. But I can't guarantee the Canon materials are exactly the same. Caveat emptor.)

To clean the lenses and camera interior, you'll need the following:

• A lens blower. This is extremely useful – I'd say indispensable – for blowing small particles off of lens surfaces and also from the inside of the camera.
• A lens cleaning cloth. It is best to use cloths that are specifically designed for cleaning lenses (or eyeglasses). These are usually of a very fine synthetic microfibre design.
• Lens cleaning fluid if the lens elements are very dirty or greasy. Here opinions vary: some people use isopropyl alcohol, some use a proprietary lens cleaning fluid. Special "lens wet wipes" are also available.
• Possibly vinegar (acetic acid).
• Cotton buds (Q-tips).

Camera interior: the mirror box

The mirror box behind the lens mount gathers dust and dirt over time. Use the lens blower to force it all out. Do not attempt to clean either the mirror or the focusing screen: these are delicate pieces and very easy to scratch, dissolve or knock out of adjustment.

Camera interior: where the film goes

Again, use the lens blower to get rid of loose dust, dirt, pieces of film and whatnot. Be careful not to get any of the gunk into the shutter, though! Finish by swiping with cotton buds if necessary, paying special attention to the film guide rails above and below the shutter (a cotton bud soaked in alcohol or lighter fluid is very effective here).

(Note: the seals between the body and the door decompose over time and are in all likelihood pretty much reduced to a gooey substance by now. If you notice any light leaks when using the camera, you'll need to replace these, another relatively simple DIY task.)

Camera interior: battery compartment

Don't neglect to clean the battery compartment. A number of electrical problems with cameras are the result of corroded or dirty battery contacts. If there is corrosion, use vinegar with cotton buds to get rid of it. Don't use the lens blower here: if there is dried up corrosion here from batteries, you don't want to breathe that stuff.

Lens surfaces

Extremely important: Before doing anything else, use the lens blower to blow any loose particles off the lens surface. You don't want any of those particles around when swiping the lens with a cloth or a wipe, or else you run the risk of scratching the surface. Then, starting with the front lens element:

• Breathe on the lens to moisturize it, and gently wipe using the dedicated lens cleaning cloth or a lens wet wipe, working in a circular motion from the inside to the perimeter of the lens. The key is to apply as little pressure as possible.
• If the lens is still dirty, repeat procedure, ideally using a different portion of the cloth.
• If the lens is still dirty, apply a small amount of lens cleaning fluid or alcohol to the cloth (or a cotton bud), never directly on the lens surface, and wipe again gently.
• This should be enough in most cases, though if the lens is very smudgy (e.g. lots of fingerprints), you may need to repeat the procedure still. The key is to work in small increments, and to never wipe the lens with a bit of cloth that's already soiled.
• Next, do the same to the rear element. Exercise caution: scratches on a rear element degrade image quality far more than scratches on a front element.