As with the knit stitch, the needles now need to switch places in order for you to move the loop off the left-hand needle and onto the right-hand needle, but this time the right-hand needle needs to go from front to back instead of back to front.
The task is performed in exactly the same way: just slide the right-hand needle back so the loop comes close to the tip of the needle. As the needle is about to slide past the left-hand needle, give it a little push to help it move to the back.
Make sure at this point that the original loop is still on the left-hand needle, the new loop is on the right-hand needle, and the working yarn is in the front.
Then just slide the loop off the left-hand needle and you've completed one purl stitch.