It varies by airline and airport, and sometimes apparently by alignment of the stars, or something. I personally have encountered the following:
- Take stroller to door of aircraft; collect at door (or nearby) on disembarking.
- Take stroller to door of aircraft; collect from baggage carousel (or mysterious and generally well-hidden "oversize baggage" counter).
- Check stroller in with rest of baggage at check-in counter; believe lies/ exaggeration about availability of airport strollers "just over there".
- Check stroller in with rest of baggage at check-in counter; don't believe lies/ exaggeration about availability of airport strollers "just over there"; get into shouting match with check-in agent.
- Take (small, umbrella-style) stroller onto aircraft, stow in overhead bins.
It is most common to be able to take the stroller to the door of the plane; unfortunately it is also very common to then be unable to get any reliable information on where the stroller will show up at the other end. It may be at the gate, or at the carousel, but nobody will be able to tell you for sure.
There is an old but entertaining and still more-or-less valid thread on strollers
here.