You download the apps from Apple or the Google Play store (free) and install them on your phone.
I
strongly suggest that you have
both apps on your phone. Fares usually vary a little bit between companies, and both companies offer promotions which will be of value. The vast majority of drivers drive for both companies simultaneously -- so there is no difference to a rider most of the time...except price.
I also suggest
all adults in your party have
both apps on their phones. Multiple accounts = multiple promotions = savings.
Before you actually activate your accounts, you might check with friends and family, because one of them may be able to give you a referral which would give both you and them some promotions.
Before you order rides, you will set up your account, select payment methods, etc. for each account. Very simple process, only takes a couple of minutes.
Look at both companies websites for information about how to order rides, and try it a few times before you actually order. You can go through the very quick process, see available vehicle types and fares, and do everything except actually order. That will give you some familiarity.
You should also talk to friends who use both services to get some tips. It's very easy, and by the time you've taken 2-3 rides, you'll be a pro.
On ordering rides, it is possible to pre-schedule rides, but DON'T. "Scheduled ride" actually means nothing and is more likely to cause you a cancellation charge than anything beneficial. Never order a ride until your entire party is at the pickup site and ready to get into the car.
Specific to WDW, there is this thread:
https://www.disboards.com/threads/everthing-you-wanted-to-know-about-uber-lyft-at-wdw.3443634/
Keep in mind that the thread is more than 4 years old, so many of the older posts contain outdated information. The same is true of info provided by well-meaning posters here on the DIS. A poster's experience from a year or two ago may well be exactly the opposite of today's situation, so be sure you're evaluating current info.