Starting Thursday, anyone in Arizona can call 1-833-USE-UBER (that's 1-833-873-8237) to book an UberX, Comfort, Black, SUV, and Assist or WAV rides in some cities for people who need assistance or who use a wheelchair. The number is supposed to help those without a smartphone or who don't or can't use the Uber app, for whatever reason.
If you want to call an Uber you call the number (did you memorize it yet?) from a cellphone that can get texts. A live human will pick up. You give your credit card information along with pickup and drop-off info. The support person will give an upfront price estimate. If it's your first time ever using Uber you'll have to confirm a verification code and agree to terms of service.
Then you're sent text messages with all the pertinent Uber information (license plate number, driver name, ETA, and such) without ever opening the Uber app. Almost everything is the same as the traditional Uber app experience, except for tipping. For now, if you want your driver to get tipped, bring cash.
My comment: Right now though anyone can actually book an Uber for someone else using the app - you just make sure you select the correct start and end destination (even if in another country). You'd use one of your linked payment methods and would need to inform the rider what description car and driver will be arriving. It's not ideal but will do the job remotely for anyone.
Got a pen? It's 1-833-USE-UBER.