After playing with a few Pro tier players over the past few days, I've noticed that some players will use their putters from the fringe or fairway.
I would recommend against using the putter from the fringe or fairway (unless you're literally right at the edge of the fringe/green or if you're a putting wizard), and instead use the chip, pitch, or flop shots instead. Judging distance needed to putt from the fringe is tricky, particularly if you have a bit of fringe to putt through in order to make it to the green.
The type of shot you choose to use from the fringe is dependent on how far you are away from the green and distance to pin. I exclusively use the pitch shot, but there are great players here who swear by the chip shot. I'd probably try it, but I am very effective with the pitch shot from inside of 20 yards so I've never really had a reason to use the chip shot. Of my 100+ holed approach shots, the vast majority have come using the pitch shot from around the green, and every pitch shot I take I expect to either come within 1 yard of the hole or, if I get a bit lucky, sink it.
Iconian made a very nice tutorial which should help with your chipping/pitching:
http://www.wgt.com/forums/t/3009.aspx?PageIndex=1