Here is a copy and paste of a reply I made a few days ago. It sounds like you already know a lot of these details, but figured it might help someone:
To use the babyswap, all of you approach the CM at the line entrance. Show her the toddler. She'll give you a paper babyswap pass. Sometimes she'll give it to the person waiting, sometimes to the person riding, and sometimes the person riding will get a special card to turn in for the babyswap pass at the loading area. It doesn't really matter, just go with whatever the CM says.
The baby swap pass is good for up to 3 people to ride the ride through the fast pass line. They typically expire at the end of the month, so you don't need to use it right away.
Note also that you can use FP and babyswap in combination, but you don't have to. The first group of riders can ride with a fastpass or can go through the standby line. It doesn't have any effect on the second group of riders.
Here's an example of a way to maximize fp/babyswap for your family:
Adult #1 and Big Kid gets FP for Rockin Rollercoaster
Adult #2 gets FP for Tower of Terror.
Baby doesn't get any fastpass anyway
Everyone approaches Rockin Rollercoaster at FP time and gets babyswap pass.
Adult #1 and Big Kid ride Rockin Rollercoaster
Adult #2 and baby go on their way to ride another ride, eat ice cream, or whatever.
Later on (whenever), Adult #2 and Big Kid ride Rockin Rollercoaster.
Everyone approached Tower of Terror at FP time and gets babyswap pass.
Adult #2 rides Tower of Terror alone.
Adult #1 and both kids go eat ice cream.
Later on (whenever), Adult #1 and Big Kid ride Tower of Terror.
Benefits: Big Kid rides RnR twice and everyone rides two headliners while only using one fast pass.
Cons: Adult #2 has to ride ToT alone and the family spends a lot of time split up.