Cast on however many stitches you like, using the smaller needle.
Knit 1 row with the smaller needles.
Knit 1 row with the larger needles.
Continue working in this manner; when you are ready to bind off, work a row with the smaller needles, and then bind of as you normally would.
Experiment with different yarns and needle sizes to find what effect you like best. Have fun!
Here is a video on this knitting technique. In the video I use Sugar n Cream cotton with a US Size 10 and 15 needle. I basically just repeat the info here in the post.