After a player runs with or catches the ball, however far the ball itself got is where it will be "spotted" or placed for the start of the next play. This is pretty straightforward most of the time. Sometimes though, a player might catch the ball and then get knocked backwards with it and get tackled further back.
It doesn't matter - it's called "forward progress" - so as far forward as the ball progressed, that's where the next play will start!
Sometimes on the TV replays, you'll see them zooming in on the ball to figure out how far forward progress took it (especially important when the team only needed to go a short distance).
SIDENOTE FROM TODAY...
Quarterback Brett Favre (pronounced like FARVE but that's not how it's spelled) came out of retirement (again) and signed with the Minnesota Vikings. This is important for various reasons including: Favre played for the Green Bay Packers for most of his career and they are rivals of the Vikings; also Favre is an older player so it is a question to how well he'll actually play; and also he will be starting in the preseason game on Friday. If you want to know more, turn on ESPN or NFL Network (or visit their websites), they'll all be talking about it.