At the beginning of just about every line, there is a cast member. That CM is there to answer questions and also has a pocket full of baby-swap passes. You go up and tell them one of you is staying with the baby and they give you a pass; then one of you gets in line. I have gotten baby-swap passes for BTMRR, Splash, Space, Buzz, M:S, Test Track, and TOT. For Star Tours, you all wait in line and then perform the swap as the ride changes. They will let your older child or other members of the party ride with you; a swap pass lets you bring 3 people on (I have gotten people out of line to come with me) and at Star Tours they just let your friends stay on the ride. I don't think they offer them for rides anyone can go on, although if you had a tiny or frightened one who didn't want to go on, say, Peter Pan, I expect if you asked they'd give you a fast pass or handwritten line pass.
The first time we went our kids were almost 4 years old and 9 months old. We had a great time--we rode almost everything.