How to tighten the a/c compressor belt on my 99 gmc sierra

The belt on that A/C compressor should be automatically tightened by the belt tensioner. If the belt is not pulled tight by the tensioner then you probably need to go get a new one, or even snag one from the local junkyard. On the other hand, if some work has been done recently where the belt was removed. There is a chance that the tensioner may have been taken off and put back on incorrectly (I've seen it before) or maybe even something blocking it from returning to it's proper position. A test to see if the tensioner is any good is to just grab onto it (while the truck is NOT running please) and give it a tug. The spring inside is quite strong and should be difficult to move. if it will move under the pressure of your hand then you probably need a new one. Another possibility is that if the belt was taken off, it wasn't put back on correctly. With all the idlers and pulleys and such in there it's easy enough to miss getting it over one of them, and that could definitely allow enough slack for the belt to slip. There should be a belt diagram under the hood that shows the path of the belt. Take a look and just make sure it's sitting exactly where it should be.