Yes, it is illegal to pump your own gas in Oregon (minus a couple of specific circumstances, like if you drive a diesel vehicle or motorcycle). You can pump your own if you are in some parts of rural Eastern Oregon, and only between the hours of 6 p.m. – 6 a.m., and only where specifically designated…so in most cases you won’t pump your own gas. 😉
As for how to do it, just pull up to the pump like you normally would, only you don’t have to get out of your car. An attendant, usually in a reflective vest, will come up to your window and take your credit/debit card, usually ask your zip code on your card, run it at the pump and print you a receipt (if you want one). You should also let the attendant remove the nozzle when it’s done pumping because they are supposed to handle it from start to finish, or the station can get hit with heavy fines if they don’t.
I hope that helps answer your question!