One of my crochet books has a bikini pattern that's lined. It doesn't provide much direction, though. However, here's what it says to do:
Cut the lining 1/2" larger than the piece you want to line. Fold edges of lining 1/2" under on all sides and pin to WS of garment. Whipstitch lining into place.
I would probably press the 1/2" seam if the fabric can be pressed. That makes it easier to keep that part turned under as you sew it on.
You might search for videos on how to add lining to knitted pieces.