Once you've sewn gathers, the edge can be wide and messy. You've worked with this fabric so much that it often starts to fray before you're done gathering it up. It will only get worse over time.
One of the more traditional ways to finish gathers is to trim the seam allowance to 3/8" and do a zig-zag stitch over the edge. This is fine, but it will look a little fuzzy over time. You can also use a serger if you have one and like to use it. I have one, and I actually almost never use it.
This is the ruffle on a dress that I finished with this method about two years ago. It has been washed quite a few times, but not tons. I don't expect it to fray any more than this, but I don't love the fuzzy look. Yes it is on the inside, but if you really love making things look fabulous on the inside, keep reading.
Step 1: Gather fabric and sew it onto whatever it will be sewn onto using a 5/8" seam allowance. You could do 1/2", but that may be a little trickier later on. See a tutorial on two methods of sewing gathers here.
Step 2: Trim the gathered seam allowance only to 1/4". Leave the ungathered fabric intact, creating a flap.
Step 3: Using your fingers, fold the flap over to meet the trimmed edge of the gathers, shown here with a mechanical pencil so you can see what's going on....
...then fold it over again. Sorry this pic is a little fuzzy, I didn't realize it when I took it. I do this just a little at a time as I go, it would be extremely difficult and tedious to pin.
Step 4: Sew in place. I use a zig-zag stitch because I don't have to think as hard about where the stitches are hitting, and it really flattens the bulk well. A straight stitch would probably well too, I just don't do it that way. Be careful that your zig-zag doesn't go over your straight stitching line--keep that to the left of the needle.
Here's the finished gathers. Pretty slick, I think.
Just FYI, the judges at my county fair really liked this method on a dress I made last year.
Here's what they look like from the outside.
Much better than this, don't you agree?
Another option: If you have a hard time folding the seam allowance over twice, or if you used a 1/2" seam allowance and don't have enough fabric, you can fold it over once and zig-zag in place. It will fray a little, as shown here, but still looks very nice and encloses the gathered seam really well.
Good luck sewing and finishing gathers!