Here's a little synopsis of the first few eps (I'll go in order)
Spoiler alert!!! If you haven't seen season one you'll probably be spoiled.
"Quantum Leap":
Sept. 13, 1956 and Sept. 1968
The pilot was a two parter and just the beginning to the madness
In the beginning there was Sam Beckett, only Sam Beckett had not a clue as to his identity. In fact he doesn't remember anything at all. He wakes up to find out that he is "Tom Stratton", an Air Force test pilot with a son and a pregnant wife. Funny thing is, he's pretty sure he'd remember something like that, right?
The only thing he does seem to remember is that he's not Tom Stratton and he's not in the Air Force and he certainly doesn't know how to fly. To make matters worse there's a strangely dressed man following him around calling him "Sam" and no one else seems to be able to see him.
Al eventually manages to get through to him and even helps Sam fly the experimental supersonic aircraft Stratton's supposed to use to break Mach 3. Oh, and Sam's supposed to find a way to stop Stratton's wife from delivering prematurely. Piece of cake.
At the very end Sam leaps into a baseball player, Tim Fox, in the middle of the last game of his career. (1968)