Safety First when using a chainsaw, it is the most dangerous tool one can own without having to be licensed or have a permit to carry.
A few quick tips: wear ear and eye protection, steel toed boots, work gloves, and if possible, a hard hat. Read the instructions that came with your saw, the booklet that came with my Stihl is quite good.
Full disclosure: I am not a professional lumberjack, just a DIY guy who wants to get people to pay attention to the proper way to use a chainsaw. One thing that is not in the video, but you should wear a helmet with a face shield and ear protection built in. I bought one for about $45, so go do it, one piece of equipment takes care of your head, eyes, and ears.
There are more than a few opinions on how to cut down a tree, I've changed the method seen in this video, in this how to cut down a tree video, i use a slant cut on the back side of the tree, and i now use a straight cut just above the front wedge cut. Slant cuts can cause the tree to twist when it falls, which is a very bad thing.
We have more tree felling, cutting down a tree, chainsaw use videos here on the site, watch them all.