Not a dumb question at all! No, you do not need a serger. A serger makes it quicker/easier, but it's not necessary. You can either turn & topstitch (will define that below) or just zig zag around the edges. I've made soakers, mama pads, and a fitted diaper using the zig zag method, and they've all worked just fine. They're not as pretty as serging, but since they're just for me, who cares?
If I were to sell them, I'd want to use a serger or turn & topstitch though.
Turning and topstitching means you sew the fabric right sides together (so it's inside out while you're sewing), and you leave an opening big enough to turn it rightside out again. Once you're done sewing that way, you "turn" it rightside out, then "topstitch" around the edge to make it look nice. Topstitching is just a straight stitch close to the edge.
I guess the best way to describe it is to think of a pillow case. If you turn it inside out, you'll see it's sewn along 3 sides, leaving an opening on one side. If you wanted to add stuffing and close up the pillow case, you'd turn it rightside out again, then sew the opening shut after stuffing. Although with a pillow, you don't usually do the topstitching part.
When sewing that little opening shut, you need to kind of tuck the seam allowance (the area of fabric between the stitching and the edge of the fabric while the fabric is inside-out) so that it looks kind of like the rest of the seam allowance, then topstitch it closed.
If you need pictures, I could probably Google something up.
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