Basically, just tell the CM at the ride entrance that you want to do a baby swap. The CM will give you a ticket that says Child Swap on it (it looks like a fastpass ticket). One of you waits with the child while the rest of your party goes in the regular standby line to do the ride. When your party exits the attraction, you switch places and enter the Fast Pass line, giving the child swap pass to the Fast pass line CM. I believe that they will allow up to three people to ride an attraction with the child swap pass. The CM's will give you any special instructions if there is a variation on that particular ride, but usually you just wait somewhere outside the attraction (near the exit) for your party to exit.
I hope that makes sense! Have a great time.
Cheryl