Fastpasses in more detail.
Some rides will have Fastpass signs - not all rides have Fastpasses available. For those rides, there will be a clock with "fastpasses being issued for" and a time. If the time works for you, take the park tickets of everyone in your party and pass them through the machine. It will spit out a Fastpass ticket for each person. Look at the time window and remember it. Put everything (park tickets and fastpasses) away safely. Now go do something else (eat lunch, go on a less popular ride, or wait in line for a popular ride - whatever). When the time on the fastpass comes, go back to the ride and enter the fastpass line. This is the "cut to the front of the line line" and often entails no wait at all - but you will sometimes have a short wait anyway (wave to the people who haven't figured out the fast pass system - if you have a three minute wait - they have a 45 minute wait).
You can only have one fastpass per park ticket at a time, so when you get off the fastpass ride, get a new fastpass ticket - for the same or a different ride.
Your DD won't have a park ticket - don't worry about it - she will be able to board any ride with the rest of your party (unless there is a height restriction).