This is by far my favorite method of seam finishing. There are some who sew the actual seam with the serger. I prefer to sew the seams on my regular sewing machine and then go back and finish the edges on my serger. I feel this gives me a more accurate and sturdier seam. I place the raw edge of the fabric so that it is just barely trimmed by the knife on my serger.
Finishing Without a Serger
Even if you do not have a serger, it is still possible to finish your seam edges on your regular sewing machine.
The first method is to use an overlock stitch which you may have on your machine. Consult your manual to see which stitch number to use. Mine is stitch number 18 on my Pfaff machine.
To use this method, first sew your seam with the designated seam allowance. Trim the seam a little if desired. Then go back over the seam using your overlock stitch. Allow the needle to go off of the fabric to the right and use the center of the foot as a guide for the raw edge of the fabric.
If you don't have an overlock stitch on your machine, but you do have a zigzag stitch, you can still finish your seams.
This method is called a zigzag rolled seam.
To do this, again, sew your seam with the designated seam allowance. If you would like, you may trim the seam a little. Then choose your zigzag stitch on your machine. Set the stitch width slightly larger than the default setting and set your stitch length very short. It should be almost as short as it will go. Go back over your seam using the center of the foot as a guide for the raw edge of the fabric and allowing the needle to go off of the fabric to the right.
(I forgot to do the original seam on my sample before I took the picture, but you get the idea)
The finished seam will look like this.