Pin or hand-baste. Use ball point pins (less damage to the fabric). Hand basting is actually quite quick (long stitches) and is easily removed.

Also, when sewing nylon, similar synthetics, or silk, remember that these fabrics dull the sewing machine needle really fast. Change said needle after no more 5 hours of sewing.

I'd be hesitant about using old coated nylon; the coating deteriorates and cracks off. Give it a good sniff first--an "off" odor is one of the first signs. Of course if this is just a "practice" run, that's different.