If you're lucky enough to have decent medical insurance I'd simply bring it up to your primary care doctor for a referral or sleep doctor in your area (you usually don't need a referral if you want to seek out a sleep doctor directly).

They will have you come in for a visit to talk about your symptoms and evaluate you, then usually they'll schedule you for an in-home test, which means you get a little device to take home and strap to your chest. It'll have a pulse-oximeter you connect to your finger, and an air flow meter that you run to your nose using a nasal canula.

If this isn't conclusive or something else seems to be going on they will bring you into the lab to sleep with even more devices connected to you measuring brain waves, muscle activity, etc. These usually look like a hotel room so it's not too uncomfortable.

I wanted to get a head start on my own so I set up a camera that has night vision to record myself since I happened to have one. (Lots of home security type cameras will have a night vision mode.) It wasn't particularly conclusive, I couldn't really make out that my breathing was stopping, but it did make me realize I seem to wake up and move a lot. Additionally I was surprised to learn I sleep with my mouth closed, since I've always gone to sleep with it open.

There are options I've seen online from various online CPAP stores to order an in-home test as described above, I don't know how reliable they are, presumably they mail you the kit and you mail it back.