Now that you have both strands of yarn attached to the needle, all you have to do is perform the long-tail cast on as you normally would, holding one strand of yarn around your thumb and the other around your index finger.
As you can see from the picture, the yarn that is around the thumb comes back to the front of the palm and the yarn around the index finger comes back to the front as well. I hold down both strands lightly with my ring finger, but you may find a way to do this that is easier for you.
Once you have the yarn in place on your hand, it's a simple matter of putting the needle under the strand on your thumb, going over the strand at that's over the index finger and looping back underneath and pulling the stitch through (I know it doesn't sound simple, but if you're familiar with the long-tail cast on -- and you should be before you try it this way -- it is).
Continue in this way, casting on as many stitches as you need for your pattern.