Proper way to ask someone to write a letter of recommendation for college admission, also, should I give them an address envelope?

US universities will want your LOR from core subect teachers who have taught you. Some may take one of them from your HS counselor.

Check with the universities you are applying to. My daughter applied to six schools. She made copies of her LOR and sent them herself to each school. Most universities want everything sent via Internet now.

I would hope you know how to politely ask for a favor from a superior.
Even though many recommendation letters are sent electronically these days, you should still provide a stamped, addressed envelope just in case the person prefers to send their recommendations the old way, unless the application demands electronic submissions only.