The stroller rental is at guest services just inside the front gates of each park. You pick them up and return them there at each park. If you are using parkhoppers - you can get strollers at each park you are at that day with no problem.
If you enter a park in the evening, sometimes you can grab an abandoned stroller in the park that someone just didn't want to return. I've never done that, but have heard a lot of people do it.