How do I find out if I have pet dander in my house?

Mostly research test. It's usually not necessary to test to see if you have pet dander. If you have a pet, you have pet dander. If you don't have a pet, some houses still have detectable cat allergen even when there has not been a cat there for substantial amounts of time. Testing is usually done mostly for research purposes though. You can take measures to mitigate, like hard floors or hepa filters, without testing.
Pet dander in house. If you have a pet, you have dander. You can also bring it home on your clothes if you visit people with pets, but the amount is small. Pet allergens come from skin and sometimes saliva and other body fluids (for your pet rat, the main allergen is urinary albumin). You can't see allergens, but your immune system can detect them in the air when you breathe them in. The more pets, the more allergens.