The Canon AE-1 cameras are unfortunately quite prone to mechanical and electronical failures.

If you don't see anything through the viewfinder, it sounds as if the mirror is stuck in the upper position. If you are lucky, a relatively easy to fix problem is that the rubber strips along the edges of the mirror box (they are there to dampen the movement of the mirror before it hits an edge) are starting to disintegrate and are getting so sticky, that the mirror clings to them instead of moving freely. There can however also be many other internal mechanical failures in the shutter mechanism.

If there is a more serious failure sometwhere, the AE-1 is unfortunately also quite difficult and tedious to disassemble and unless you are well above average versed with tiny screwdrivers and tongs, this is not likely something you might want to fix yourself. You can always google 'canon ae-1 mirror stuck up' or 'canon ae-1 lever stuck' and find many discussions about these problems in other fora, but as I said, there are so many possible causes for your problem, that it is impossible to tell without taking the camera apart and start looking for the actual cause.

If you want to keep the camera, you might rather want to find someone willing to repair it instead. But in that case, also a repair shop might not be able to obtain any required spare parts. Since AE-1 camera bodies are abundantly available and not very expensive, you might also rather consider getting a 'new', used camera instead.