Grab an old tee shirt or scrap of fabric similar to your shirt. get a scrap of your red spandex. pin them together and practice sewing them. Use the stretch stitch setting on your machine. The advantage to spandex is it doesn't fray, so you can just top stitch it in place without worry.
Put on the shirt.
line up where you want your red panels (you need either a mirror or a buddy)
pin the panels in place ( don't stab yourself)(don't bleed on your costume)
Make sure the panels are stretched about the same as the shirt. You will probably need a lot of pins to really keep it in place.
Take it off (duh)
use a stretch stitch on your machine right on top of the raw edges of your red panels (don't sew over your pins, it's bad juju)