You do not need to have a smartphone; many do not (my mom visits WDW without one and does just fine!).
At a quick service restaurant, you just tell the CM at the door that you need to order at a register. Every quick service has at least 1 register open that you can place an order at, the old fashioned way. You'll wait for your food like you used to.
If you are dining at a table service, you can check in for your reservation at the host stand just like you used to.
At any restaurant that directs you to a QR code menu, you can simply request a printed menu. Many of them hand you a menu anyways but my MIL requested printed ones at places that didn't. They have a stack of them and it's not a problem at all.
Hope you have a great trip!