The zigzag stitch on your sewing machine can neaten the seams on your sewing projects and help prevent the fabric from fraying. It's a great option for beginners as it's relatively simple to do and particularly useful if you don't own an overlocker. It's how I was first taught to finish my seams and is a technique I used all the time before I began overlocking.
I would recommend getting an overlock foot for your sewing machine. They have a little flap of metal which helps guide the raw edge of the fabric and makes it easier to get the stitching in the right position.
Here's how to zigzag finish your seams:
1) Stitch your seams as normal, then trim them down by a few mm (don't go crazy here, you need some width to accommodate the zigzags).
2) Set your machine to the zigzag stitch setting. Put your overlock foot on your machine. Test the width and tension of your stitch on a scrap of fabric and adjust if necessary (it's different for different machines, your manual will tell you how).
3) With the raw edge of the fabric touching the little flap of metal on the overlock foot, stitch along one of the seams. If you're using lightweight or sheer fabric, you may want to stitch both seams together as one, otherwise you can do each seam separately. The right-hand point of each zigzag should just reach the edge of your fabric. Don't back tack at either end - instead...
4) Tie the loose threads at either end in a double knot to secure them, and trim.
5) Press the seams either open or to one side (depending on whether you stitched them separately or as one).