Hi, not sure if you've got some answers to your question already but here goes...
Some saws have an adjustment dial, usually on the right hand side of the saw, that pulls or pushes the bar out slightly which in turn tightens or loosens the chain, depending which way you turn it. The chain should NEVER sag underneath the bar. You should be able to pull the chain down around 3mm to 4mm when the chain is cold, but no more, underneath the middle of the bar.
A new chain will need more regular checking and adjustment for tension than used chains.
Other saws have a small screw which you can tighten on the inside of the bar with a screwdriver or other tool. Clockwise tightening will tighten, anti-clockwise will loosen.
On some saws you need to remove the side panel to gain access to the bar adjuster.
If you need any more info, please could you supply the model you have and I'll be happy to help.
JP Clarey, September 2010