Scenario: you’ve finished leading a pitch, and find yourself on a big ledge. You see nothing near the edge to use for an anchor, but 10 (for example) feet back from the lip there’s a nice big tree. You want to build an anchor on the tree, but then belay from the edge of the cliff. A belay from the cliff edge lets you see your partner, minimize rope drag, have better belay communication, and who knows, maybe even toss the occasional pebble at them if they are making it look too easy. =^)
Here’s one of several good way to rig that (and no, you thankfully don't need a heap of 1 inch webbing!) This assumes you have at least about 15 feet of rope left after your lead.
Walk over to the tree, put a sling or cordelette around it, clip a locking carabiner or two to the sling, and clip the rope through the carabiner(s). Walk back toward the cliff edge. You’re still on belay the entire time. (Another way to rig this is to skip the sling and biner and just walk around the tree, assuming you can easily do this, and the tree is not going to get evil tree sap on your rope. If it’s a conifer tree, a sling might be a better choice.)
When you get close to the edge about where you want to belay, pull up a few feet of slack, and tie an overhand on a bight using BOTH strands of the rope. (This is known in some corners of the climbing world as a Big Honkin’ Knot, or “BHK”.)
Done! 1) You’re fixed to the anchor. 2) it positions you nicely on the edge so you can watch your partner, and 3) it gives you a nice master point from which you can belay your second or set up a hauling system on a big wall. (Note the ATC Guide clipped to the overhand loop, ready to belay up the second.)
One caution, because of the dynamic rope, keep in mind that if your second takes a big fall, the rope might stretch enough to potentially pull you over the edge. Try to keep a tight rope on your second when belaying, use an auto locking belay device such as a Black Diamond ATC guide, and try to brace your feet a bit on something if possible.
One other possible enhancement: If you have any concern about your ropes running over a sharp edge, or rockfall onto them, or if they might get damaged in anyway, or if redundancy simply gives you a warm fuzzy feeling, you could tie an overhand knot at the anchor point, giving you two redundant strands.
Here’s a related technique that's more suitable when using double ropes. Put both strands of rope through the anchor, walk back to the edge, tie a double overhand loop for the belay, tie another a double overhand loop and clip it to your harness. See photo below, contributed by Alex Kostadinov; thanks Alex!
A reader mentioned to me that there is an excellent article about this at climbing.com, called “belay extensions.” Read it here.
This technique can also be used for a big wall climbing, to rig a hauling a point to minimize friction. True life story: my partner and I had topped out on The Prow, a classic big wall route in Yosemite. The last pitch concluded in a series of fourth class ledges. We set up our anchor on a tree above the ledges that made our hauling absolutely miserable from all the extra friction. Following us on the route were a team of two New Zealand mountain guides. Their leader finished, went to a nearby tree, rigged the anchor exactly as shown above, walked back down to a low friction place to haul, and set up his hauling system directly on the overhand loop. He got his bag to the top with minimal cursing and much faster than we did. Lesson learned!
I can't quite remember, but I think I first heard of this tip in the excellent book “Rock Climbing Anchors: A Comprehensive Guide” by the late Craig Luebben.