Airline Rewards

My traveling in Europe and Egypt in January. When I got home, there were people trying to make me sign for a credit card with rewards. They said that even miles to where I came from would be rewarded. I did not sign because I heard the opening of credit accounts is too bad. Now, I'm interested in this. Is it possible to get any kind of mileage reward (reward credit card or airline miles) for my trip, even if my trip is over?

Yes, quite possible. When you register go to earn miles. Then there will be an option, enter Travel past. Click on the type and your confirmation number. I did this several times.