Okay, this happened to me last year. This is what I did, and it worked (meaning no stain left and no smell left):
I took a few big sponges and soaked up as much pee as possible, rung them out, cleaned them then dipped them in warm, soapy water and went at the mattress with that. I repeated putting warm soapy water then soaking up the water with a towel then doing it again about 3 times. I then just used water to rinse it, then I soaked up as much moisture as possible with more towels and when it was dry as it could get with the towels I stood the mattress up against the wall, had a fan facing the wet part of the mattress and kept it on there all day until it was time for bed (I started the process in the morning of the accident).
It worked well. Just make sure the mattress is fully dry or else it will develop a moldy smell. Steam cleaning may push moisture too far into the bed, I don't know... All I know is that my method worked. Maybe there's an easier one out there, though?