I used to be a fan of turned under and topstitched finish until I started doing the bound edge. And now I am a total convert. Actually I have been a convert for a while. I just didn't realize that there is no tip on how to do it here. Actually its no rocket science but sometimes it's helpful to direct people to a tip rather than explain it. So here's how I usually do bindings on my knit tops.
Step 1: Measure the circumference of the neck or armhole on the stitching line (not on the cut edge). For example lets say it's 21 inches. Now add 1/2" more to this (for 1/4" seam allowances). So our total is now 21.5"
Step 2: How stretchy is your knit? If its fairly stretchy like onionskin you can easily subtract 2" (sometimes even more from this measurement. Otherwise subtract 1" from it. So lets say we are doing this on an onionskin, our final measurement is 19.5". Now cut one strip (two if this is for the armholes) on the crosswise grain of fabric. Width of the strip should be roughly 4 times the final width of the binding. This binding will be seen from the right side of the fabric. I usually do 3/8" or 1/4" bindings so I'll cut my strip 1" X 19.5" .
Step 3: Sew this in a circle, joining the short ends together (Right sides together). Press seam allowances open. I like to do this on my sewing machine - much less bulk, but you could certainly use a serger. In that case you would press the seam allowances to one side.
Step 4: Find the center front and center back of your neckline. Now you need two more marks to quarter the top. Mark similarly on the binding.
Step 5: Pin the binding to the Neckline Right sides together matching the marks. Stretch the binding evenly.
Step 6: With binding on top and the neckline or armhole towards the sewing machine/serger bed, start stitching. Sew all around the neckline again stretching the binding evenly to match the neckline. I usually just use a tiny straight stitch for this.
Step 7: Fold over the binding on the seam allowances and to the inside so that the binding is visible on the Right side of the garment. Press and pin again. I like to press on a curved surface - like a sewing ham.
Step 8: Finally stitch in the ditch from the right side to secure the folded over binding to the inside of the top. This means Finding the "well or ditch" of the previous stitching and stitching right in the center of it so its virtually invisible. Its very easy to do this if you use some kind of a edgestitching foot. Since we are using a knit, the raw edge inside won't fray, but if your knit ravels, finish one long edge before doing all this.
Step 9: Give it a final press and admire your work :)
Nine steps seem like a lot of work, but once you do this technique you will see how easy it is. I really like it because even if there is a slight chance of gaping, with this method its taken care of.
The photo which I have attached to this tip is a good example of what it looks like. Remember that the binding should always be slightly smaller than the neckline/armhole circumference.