Question: How tight should the chain saw chain be?
Answer: There isn't an easy answer to this, but a little common sense can go a long way. You don't want it dangling off the bottom of the bar, as this increases the wear on both the bar and the chain, and also increases the possibility that it will come off. You don't want it super tight, because it will be putting unnecessary stress on the sprocket, bar, and chain. Rotate the chain a time or two on the bar to take up any slack at the sprocket, and tighten the chain 'snug' to the bar.
In general, you should be able to grab the chain directly by the "drive link" in a section of the chain near the center of the length of the bar and by pulling with a moderate amount of pressure you should be able to "just clear" the tip of the drive link from the bar. When I saw "moderate amount of pressure", I mean grabbing the chain rather loosely with the thumb and fore finger and pulling it away from the bar. Perhaps about 1-2 lbs of pressure should suffice.
If when you start the chain saw, you hear a "whine" coming from your bar and chain, then it is normally safe to assume you have over tightened the chain. Loosen the bar and readjust your chain to the proper tension.
For details on the proper technique for tightening the chain, see the "
Saw Chain F.A.Q.: How do I properly tighten my chain saw chain?" section.