Plenty of good advice already. I will put some links in for two products that drastically improved my ability to sharpen chain saws (and other things)
One is the (previously mentioned) asian electric chain saw sharpener.
http://www.harborfreight.com/electric-chain-saw-sharpener-61613.html
I have owned and used one of these for about a decade now. It is a surprisingly effective and capable tool. $34. It takes some practice to set it up, and to sharpen the correct amount.
There are a ton of videos on how to do this. And double extra reinforcement about this being a two step process. You have to sharpen each tooth, and you have to (ever so slightly) file or grind down the depth stops ahead of each tooth. I find that I do 5 or 6 sharpenings before I notice it's not as effective at cutting. It starts to produce more like saw -dust- instead of bigger chips. Then I know it's time to adjust the depth thingees.
The second product that had a huge impact on knowing when the object is really sharp(knife, chain, scissors) is a triplet lighted magnifier. Once you see the cutting edge, before sharpening, during sharpening and after sharpening, it's much easier to know when you're done.
The glass triplets are about twenty bucks on ebay. Even the 5 or 6 dollar loupes are better than just trying to eyeball it.
http://www.ebay.com/itm/10x-Magnification-Magnifier-Jeweler-Loupe-21mm-Triplet-Lens-6-LED-Light-/221933356824?hash=item33ac424718:g:lZ4AAOSwo6lWPC~q