Its easy. Follow signs that read "trains to city" at O'hare. You will come to a bunch of vending machines at o'hare el stop. You can buy a card there. Machines take cash only and don't give change. They give you a card with whatever amount you buy. So if you are going to make two trips bring 4.50 in exact change or $5 if you want to waste 50 cents. You can also buy daily passes. I think they have 1,3,7 days. not sure on cost. Check CTA website for more info.

Blue line is train that goes to O'hare. O'hare is last stop so it only goes in one direction there. No need to change as Blue line goes all the way downtown. Closest stop to Sheraton is clark and lake. If you ever noticed the trains in the middle of kennedy expressway going to ohare, that is the blue line.