Wait for the blooming period to end and the flowers to drop off of the cactus. If you want, you can pluck dead flowers off with your fingers once the cactus is no longer flowering.
Thin out the cactus by very slightly pinching off a few leaves from each stem throughout the cactus with your fingers. Make sure you're wearing garden gloves because the leaves can be a little prickly.
Cut back three or four entire stems down to the soil with pruning shears or a sharp kitchen knife. The combination of thinning out a few leaves and cutting back a few stems will encourage the cactus to branch out and bloom again the following season.