On ice, when I reach the point where I am going to build an anchor, I usually put in a screw (or sling a drip, etc.), clip a biner to the pro, and tie myself off with a clove hitch to the biner, using the rope. I then call "off belay" and finish building the anchor. When I have a master point I tie into the master point locking biner with a clove hitch and the rope, untie the first clove hitch, and get ready to belay the second.
I hate opening the biner on the first piece of pro, which I have to do to remove the clove hitch, and it can be awkward getting the clove hitch off that biner without shifting the anchor's sling or cordellette off that biner. Also my method seems slow. Is there a better way? Something about using a sling, girth hitched to my harness and clipped to the first screw?
I have looked in my various books and somehow I am not seeing the procedure.