To keep a chain saw sharp, you must sharpen it often. This is not as difficult as it sounds - all you need are a few simple tools and some practice. There are really only 2 steps to sharpening your chain saw. First, you need to file or grind the teeth on the chain to a razor sharp edge, and second you need to adjust the height of the depth guides that regulate the amount of wood taken by each cut.
You can imagine the teeth on the chain as small wood chisels, each one taking a small sliver of wood from the cut, every second tooth cutting from the opposite side. If each tooth takes a consistent amount of wood, at the same angle, and with same amount of effort or force from the saw, then we will get a nice clean cut with a minimum of struggle. When the chain saw doesn't pull to either side and the saw cuts through the wood like butter you know you have a well sharpened chain saw.
When you're learning how to sharpen your chainsaw it's a good idea to tighten the chain so there is very little slack. This will keep the teeth straight and make it easier to maintain a consistent angle when stroking with the round file. You should still be able to move the chain around the bar in a snug fashion. Just remember to loosen the chain before using it again.
Pay attention to the cross angle of the teeth, as well as the upward tilt angle of the sharpened edge. Line up your round file so that it follows the existing angles on the teeth. Gently stroke the file towards the tooth's point (away from the saw body). Watch the guide carefully so you can keep a consistent angle. Always count the number of strokes on each tooth - usually 5 or 6 strokes is enough. Then move on to the next tooth on the chain and stroke 5 or 6 times at the very same angle.
Repeat this pattern for all of the teeth that point in the same direction (every second tooth). Then flip the file guide around and repeat the process for every other alternating tooth pointing to the other side of the saw. Remember, it's very important that every tooth is sharpened the same amount or the saw will pull to one side when you try to cut.
After several sharpenings you will have worn the teeth down slightly. The depth gauges must be filed down so they are no higher than the tops of the teeth on the chain saw. Many people don't know about this step, but if you don't maintain the correct height of the depth guides your chain saw will not cut properly.
All you do is set the depth guide on the chain straddling the teeth and a small notch on the guide will allow you to remove the correct amount from each gauge. Filing the depth gauges is easier than sharpening the teeth because you're only trying to set the height of the depth gauges, not actually sharpen them.
