With child wearing eyeglasses, carefully position a piece of copy paper behind affected lens and arm/temple (from nose to ear). Then use one of the washable markers to trace a simplified patch shape around lens and arm/temple.
Cut on traced line, then use paper shape as a template by pinning it onto felt and cutting around it. Repeat to cut another matching shape out of felt and one more out of fabric.
Trim around 1/4-inch off edges of fabric shape to make it slightly smaller than felt shapes.
Place fabric shape right-side-up on one of the felt shapes and use sewing machine (or needle and sewing thread) to stitch along edges using zigzag stitch or blanket stitch.
Fold this fabric/felt shape at approximate location of eyeglasses hinge, fabric-side inside fold, then sew across each corner about 1/4-inch in. Repeat with other felt shape.
Position fabric/felt shape on top of felt shape with all sewn corners facing one another. Straight-stitch 1/4-inch in along top and bottom edges.
Slide eye patch onto arm/temple and lens of eyeglasses.
Notes
DIY Eye Patch Tips and Tricks
A couple of tips to help ensure your child will actually want to wear their new homemade eye patch...
Choose a fabric print in your child's favorite theme (e.g., trucks, dinosaurs, Disney) or let your child choose their fabric themselves.
Make several eye patches at once while you've got the supplies out and you're in the groove; you'll want backups in case any get misplaced.
Make various eye patches in different fabric patterns/colors to give your child a choice and feeling of empowerment.
Use fabric scraps to sew a small eye patch onto your child's favorite doll or stuffed animal.