Ok, here is what I do. If the spot is still wet, I take terry cloth towels, double folded, put them on the spot, and stand/jump/stomp on them until I can't get any more of the urine out.
Then I take carpet cleaner and pour it on the spot to make it just as wet as it was the first time. Blot again with towels, again, standing on them until I can't get any more liquid out.
Then I do it again with plain water, blotting again, then put a fan to blow on the spot until it's dry.