There are some very good answers here and most of what I will say is covered.
At the beginning of this year (2008) I decided to do a "Jesus" and build a bankroll from freerolls.
I tried several different strategies. Pushing all in every hand, very loose, very tight etc.
IMO the best strategy is to play
extremely tight (even sit out if you like) in the first hour.
On sites like
pokerstars where a NLHE Freeroll has 12,000 entrants you will find that at least half, will be knocked out in the first hour. (I played in one, on a Sunday, where 10,000 were gone before the first break.)
Pay close attention to the other players at your table and see who is calling/raising/pushing with crap. Who will chase flushes and gut shot straights or just stay with overcards. Who will call a C bet,ATF, with anything.
When you get a good hand, in position, do not be afraid to push ,someone will call. You should already know what the others at your table will do.
Be prepared for a lot of suckouts and try not to get too upset when someone catches runner/runner to beat you. It
will happen.
As was pointed out , freerolls are not very cost effective as you can play for several hours for very little return. The way to combat this is to multitable as many games as you can handle. (If you are playing supertight this is not that difficult.)
I also joined a lot of sites, without depositing, just to play their freerolls.
(Warning.. Check what freerolls the site has before joining. Some only allow depositors to play.)
Hope this helps.
All the best.