How do I know if the vaccine works, without being exposed to the virus?

Three weeks after the vaccine (2nd vaccine if you get 2), you can get an antibody test to see if you have protective levels of IgG and IgM antibodies.
== you will have to continue to test to see how long the protection lasts. 

You won't.   Can't. 

You won't know if you are exposed to the virus. The point of the vaccine is to protect you if you do.

you'll know when you dont get covid

You know because of the very extensive trials they ran on the vaccines. That's how science works. Things get tested. There's no reason to think that it worked on the 75,000 people in the tests, but wouldn't work on you.