Disclaimer: This is advice from a non-professional, for informational purposes only. If you’re not 100% sure about the properness of something as safety-critical as your wheels, consult a professional.
The lug spacing (bolt pattern) is key. The offset and centerbore can be, as well.
The wheels on my VW are 16x7.5, 4x100, et35. That’s 16 inches in diameter, 7.5 inches wide, four lugs each forming a circle 100mm in diameter, and a +35mm offset. (The distance between the hub mounting surface and the wheel centerline)
My tires are 205/45-ZR16. 205 mm wide, sidewalls are 45% of tread width, and fit on a 16-inch wheel.
In general, matching the bolt pattern is the biggest thing you have to worry about. If it can bolt on, it’s more than likely going to be compatible. Strange offsets may run you into a few problems, but that’s not usually an issue on factory and conservative aftermarket wheels.
For example, I can use any Honda wheel that comes in 4x100 on my VW. Cars that have very different wheel requirements like offset (e.g. old rear wheel drive cars often have negative offsets, front drivers are usually positive) usually have wildly different bolt patterns. i.e. There’s little chance of my accidentally putting an old Camaro’s wheels on my Jetta.
Centerbor is a minor issue. Wheels made specifically for your car will have a centerbore equal in diameter to your hub. Aftermarket wheels, or wheels for other vehicles may differ. As long as the hole in the center of the wheel is bigger than your hub, you can use rings in the wheel to match the sizes up. So centerbore is probably the least of your worries.
You don’t have to match rim size, necessarily. You can increase wheel size as long as you compensate with a different tire size. they key is to keep the same overall rolling diameter. For example, a 205/45-16, a 205/50-15, and a 195/60-14 are all basically the same outside size. The difference is how much of that overall diameter is metal, and how much is rubber. But they roll almost exactly the same distance for every revolution, and that is key.
Check out The Tire Rack’s Wheel Tech Section for lots more info. They may help you find what brands an models are compatible with your car.
Using the above info as a background, check out this site for lots of vehicle compatibility information.