You would do both purls of your 2x2 rib the same way. Since you are doing ribbing in the round, you will be working the stitches as they lay -- knits will be knits and purls will be purls. Because of this, your knits will all be regular knits stitches with no changes. Only the purls will be different: For the first round, you'll be purling clockwise through the front leg. In subsequent rounds, the purls you created in previous rows will be twisted, so you need to work them through the back leg, while continuing to do them clockwise.
I hope this doesn't muddy the waters further, but keep in mind that you can use this technique with any combination of knits and purls, not just ribbing and stockinette. You just need to pay attention to the way the stitches are seated so you can correct any twisted stitches. For example, with flat ribbing, you'd be knitting the purls and purling the knits of your previous round. This means that the stitches you intend to knit into will be twisted (since they were purls in the previous round), while the ones you intend to purl into, won't (since they were knit normally). This means that you'd end up working all the knits through the back loop and all the purls through the front loop, while maintaining the clockwise wrap on the purls. It really sounds more complicated than it is because all you need to remember is this: always purl clockwise, and whenever you see a twisted stitch, work it through the back loop.