In your left hand hold the needle which has your cast on stitches and in your right hand hold your empty needle.
Take your right needle bring it to the left of the stitch closest to the tip of the left needle and push it through the bottom of that loop. Your right needle should be to the left of the front of the loop and to the right of the back of the loop.
Hold onto both of your needles with your left hand and pick up your working yarn with your right hand.
Bring your working yarn across the back of your work and between the two needles, so that it wraps around the needle which is to the back.
Pick your right needle back up and keep hold of your working yarn so it's still quite taught.
Slide your right needle downwards and you should be able to see the yarn which we just wrapped around the needle sitting on top of the needle. In the gap between the yarn and the left needle bring the right needle forwards, with the yarn still sitting on top of it.
Slide the right needle to the tip of the left needle so that the loop on the left needle slides off the end. You should now have completed a knit stitch which will be on your right needle.
Repeat steps two to seven for as many knit stitches as you need.