Hand Sewing Patch to Huge Elbow Holes in Sweater
This is what I would do:

Take the thread and whip stitch the holes so they do not fray any
further.
Since it is knit textile, tighten and loosen to manipulate the hole
in a fun or fashionable shape.
Place the patches on the inside of the garment, temporarily secure
with safety pins, straight pins or basting stitch.
Use an interesting embroidery stitch to secure the patch permanently.
Remove pins or basting stitches.
Trim excess fabric.

A fun alternative is to appliqué over the holes:

Whip stitch the holes to prevent fraying.
Secure patch on the inside with pins or basting stitch.
Cut out an appliqué shape or shapes, secure to “right” side and
stitch.

Key words/ phrases to search for:

whip stitch or blanket stitch - used to quickly sew an edge
basting stitch - long &amp; loose stitch to temporarily hold materials together
appliqué - technique to apply cut fabric designs onto material
knit textile versus woven textile

FYI: darning has been addressed in the Stack Exchange, but mostly for woven fabrics, not knits.