You can leave the edge raw for a wispy look or you can finish it off. A pencil edge, a corded edge, ribbon, lace...there are many possibilities. A serger is not necessary for a fine pencil edge; in fact I personally find the serged edge tends to look cheap and unprofessional. Here are two methods for a narrow edging using a regular sewing machine.
A rolled edge can be made by folding over the edge about 1/2" and zigzagging over the fold. Use a fine thread, like a serger thread or size 80 to 120 cotton thread, and a closely spaced, narrow zigzag. Trim away the excess tulle very close to the stitches, being careful not to nick them. Applique scissors are good for this.
For a ruffled 'lettuce edge' effect, stretch the tulle slightly while stitching; experiment with scraps to see how much you need to stretch it, then keep that tension constant for the best look.
A corded edge can be made by zigzagging over a length of pearl cotton, bourdon gimp, or satin rattail or mousetail cord. Lay the cord about 1/2" from the edge and set the stitch just wide enough to enclose it. After stitching, trim as close to the stitches as possible.
Soutache braid or ribbon can be sewn on in a manner similar to the cord, using a straight stitch rather than a zigzag. It is usually easier to sew an edging 1/2" or so from the edge and trim the excess tulle than to try to align it perfectly with the cut edge.
