If you're lunging in a saddle - slip the end of the side rein under your girth and buckle. Then clip to the bit AFTER you have attached your lunge rein. If you clip the side reins on before you have the lunge rein attached, a horse (particularly one not used to side reins) can very easily injure themselves if they get a fright.
I really think your instructor should be teaching you how to lunge in side reins though, as if you don't use them correctly, you just end up teaching the horse to suck back off the contact, or hang onto the bit, serving no useful people. It is REALLY important that you make sure her hind legs are active, tracking up and she is accepting the contact.
I am hoping the side reins are not on there to pull her head down? As that is NOT the intention of side reins.