While it's squeaking, turn on the air conditioner and see if it changes the sound or has any effect. If so, it could be the AC pulley and the clutch engaging is enough drag to stop it momentarily.
There are all sorts of methods ranging from using a mechanics stethoscope and checking ear part (while trying not to get caught up in the belt or fan) and also using a piece of rubber hose for the same purpose. In my experience, these sometimes work, but not always. First thing you may want to do it take the belt off and start it up, just to make sure it's not squeeking then. Only run it for a few seconds since the alternator and water pump won't be running.
Then try spinning each pulley (sans the belt) with your hand and you might get lucky and find a squeak.
One snag that you may hit is the tensioner pulley. On my 5.4L motor, without a belt to hold it away from the spring, it actually rubs the block. I put a breaker bar on it and wedged it against something on the battery side and that held it out enough for me to thread my new belt in when I had to replace it.
If that doesn't turn up anything, I would pull the alternator and take it to Auto Zone or one of them and have it tested. They will spool it up to a thousand RPM or whatever and you can listen for the squeak. My next step is while I am at Autozone, I 'd buy a tensioner pulley and an idler pulley (both around $20). Then put the alternator back on, and swap one of those pulleys in, put the belt on and see if it's gone. If not, replace the other pulley (remove the first if you want to return it) and try again.
If after all that you still have the squeak, you have at least eliminated alternator, AC compressor, idler, tensioner. Not you have the water pump, the fan and power steering.
I've also gotten mixed results by spraying a little WD40 or penetrating oil into the bearing area of each pulley, one at a time and see if the squeak stop temporarily.
