This is very different than picking up regular stitches, since you are attaching two pieces.
In this case, if your yarn is in the right place to begin the work, use it. If not, cut it and start it here.
Usually stitches are picked up with the right hand needle, then the needle is turned and worked the other way.
In this case, you pick up a stitch through the cast off edge onto your empty needle held in your left hand. Once that loop is on the needle, you knit it together with the live stitch on your other needle.
I'm picturing this with your needles held parallel, points facing the same way, with wrong sides facing. The side with the cast ons I think should be in the back with the live stitches in the front.
Does that sound right?