Hi, M. Go down the board a little way to a post called "Constant whining noise from outside hose faucet" or something close to that posted by Lance on 6/17. Look at my comments about a sillcock. That's what your faucet is really called.
To unsolder the sillcock you have to get all the water out of the pipe. The water acts as a heat sink and pulls heat away from the joint faster than your torch can supply more heat. Close the inside stop valve and open the sillcock. This may get enough water out of the pipe--or it may not. I have found that it is easier to cut the pipe and remove it from the wall, solder a length of pipe into the new sillcock (and take the valve stem out while you are doing this so you don't melt the rubber washer and stem seal), measure the correct pipe length and cut to length, insert the new pipe through the hole in the wall and solder the old and new pipe together with a union inside the house. Make sure that you pipe and fittings are really cleaned with sandpaper to get rid of all oxidation before you try to solder and use a flux. Other than a lot of trips between inside and outside the house, this is pretty easy to do.