How do I install a new, non load bearing wall in my basement?
You shouldn't have to do anything too special, but here are a few tips from my experience:


Use a treated board for the bottom of the wall where it touches the concrete.  This will help to prevent rotting from any moisture that may seep up from the concreate.
Build the whole wall on the ground just a bit shorter than the lowest joist/beam so you can easily raise it into place without it getting stuck.
At the bottom secure it with cement nails/ramset/tapcon screws to the cement floor.  
At the top, if the wall is perpendicular to the joists, you can shim between the bottom of the beams and the top of the wall and nail through those to attach it to the joists/beams.  
If the wall runs parallel to the beams/joists you can either put scraps between the beams and nail to those or you can attach a scrap of 2x4 flatwise to the wall and up against a stud, attach it to the cement wall, then nail through the stud and into the side of the scrap.  Do that for every other stud or so.