On the first park you go to, they should (but ask them if they don't...) ask you how many days you'll be needing a stroller. You receive a stroller voucher for each day's rental. On subsequent days, you will just go directly to the doorway where they're handing out strollers, and you will bypass the line to pay for the daily rental. Saves a few minutes, especially first thing in the morning. You will keep a ticket stub that serves as your deposit proof, and if you turn that in with your stroller at the end of the night, you receive a Disney dollar. If you are going to another park, you hang onto that ticket stub and use that to rent another stroller.
Also, if you are going to Downtown Disney, you can go to Customer Service and show them your ticket stub and receive free rental there as well. They only have singles there. Not sure if you could get 2 singles... we really only needed one at that point. Also, you will have to put down a $20 deposit for the stroller at DTD, but they refund it right back to you when you return the stroller.