I realize this is NOT the forum for Uber discussions, there is plenty of that on the Transportation board, but since you asked I am happy to answer your question!
Yes, download the Uber app to your phone. I think your first ride is free. You have to put in credit card information that is stored within the app. When you need a ride, you open the app, plug in where you want to go (it knows your location) and a little map shows you little cars indicating where the drivers near you are with an ETA of their arrival to you (usually within minutes). You can then submit a request for a ride, and up pops the driver's name, picture, information, car type and license plate number so you can identify them when they arrive. You can then watch their little car driving toward you on the map - it's actually kind of cool! When they arrive, it works basically like a taxi, except when you get out, there is no payment transaction involved. The cost, including the tip, is charged to your credit card right from the app. Super convenient! After you do it once, you will get the hang of it.
We have used WDW taxis on many previous trips, and usually spend between $18-20 with tip for each ride depending on where we are going. An example of Uber charges we incurred from Port Orleans Riverside during our stay, INCLUDING THE TIP (be aware the prices vary a little from time of day, demand, holidays, etc.):
POR to Beach Club (morning): $6.47
POR to Contemporary (evening) $7.44
POR to Animal Kingdom (early morning) $9.64
POR to Polynesian (evening) $7.16
Boardwalk to POR (evening) $7.42
POR to Beach club (evening) $6.55
We generally utilize the Disney buses (or walk or boat depending on where we are staying) for most of our transportation needs. I realize many people are very wary of private car services, with good reason, so I know it isn't for everyone. But, in my own opinion, the convenience of door-to-door service can't be beat on super hot days or when you are tired or pressed for time.