You usually have to get a car with Android Auto pre-installed if you want the feature to ever be available to you, but Hyundai has embraced Google's car platform more so than others. It just announced an update is available for some of its 2015, 2016, and 2017 models that adds Android Auto and CarPlay. You can install them yourself or go to a dealership and pay them to do it.
You'll have to log into the My Hyundai site to see if your particular model and variant is included. Versions of the Sonata, Santa Fe, Genesis, Elantra GT, and Tucson have updates available today, but compatibility depends on the infotainment package you got in the first place. The 2016 Sonata Hybrid, Sonata Plug-In Hybrid, Azera, and Veloster are supposed to have updates available soon as well.
Installing should be doable if you're reasonably tech savvy, but this is a car we're talking about. If you break something, you'll have to go to the dealership and pay them to install the software and fix whatever you did wrong. The service center installation will be available starting sometime in June. You can also grab Hyundai's new virtual guide app for Android while you're at it. The app appears to be a simple manual for Hyundai cars, but there is a somewhat interesting augmented reality engine view as well.