I live here in the LA area and use Uber religiously for getting around when I don't want to deal with driving and/or parking my car.
The idea of Uber is to eliminate the need for any cash transactions between you and the driver. All transactions are handled through the Uber app itself, electronically.
Upon setting up Uber you would choose your form of payment. I personally use my debit card information and have also linked Apple Pay as well. There is an area to add an uber gift card code as well. I believe I've seen uber gift cards for sale at my local grocery stores gift card section.
Based off your GPS Uber will identify your current location or you can manually enter this info as well. You will then input your destination address as well. You can do this by entering the physical address or by searching the name of the location, for example the hotel name. In the LA area you will be provided with the fare cost in advance so that there are no surprises in how much this trip/ride will cost you.
Upon pick up, your uber driver will start your trip/ride. Upon dropping you off they will stop your trip/ride. All you have to do is thank your driver for the ride and exit the vehicle. No need to approve anything on your phone. The payment will be automatically deducted from your form of payment you set up in the app. Shortly after the ride the Uber app will ask you to rate your driver based on a 5 star rating system, Uber relies on these as drivers are required to maintain a minimum rating to drive for Uber.
Helpful tip for LAX. LAX has recently created Uber/Ride Sharing Pick Up Zones. These are actually upstairs at the departures area. They are identified by a letter. You would select your pick up zone based on which letter is closest to your terminal. This will be easily identifiable through the app as well as the posted ride sharing/pick up zone signs at the airport.
I hope this information helps. I use Uber all the time for pick up and drop off at LAX when traveling for work.
EDIT to say: Upstairs departures area, previously I said upstairs arrivals.