Many smartphones and tablet computers are GPS-enabled. With the right app they can be used as a navigational aid. To do this, download the GPX file from the route page and import it to your device. How this is done depends on the app you’re using. The app will also determine your choice of underlying maps.
ViewRanger is popular GPS app for both iPad, iPhone and Android devices. It allows importing of GPX files (including synchronisation with Dropbox, which is very handy). It has a good selection of free and paid-for base mapping. It’s best to install the maps on your device before you go, in case you are in a place with no phone service. GPS can drain batteries fast, so it’s worth taking a paper map as a backup, at least until you get an idea of how long your device’s battery will last when being used for GPS navigation. Viewranger GPX import instructions for: Android phones; iPhone.
Using a smartphone or tablet as a navigational tool is still in its early days and can be fiddly, depending on your particular hardware setup and still limited by battery life. My view is that it’s probably still more reliable to use a paper map and/or the turn-by-turn route instructions supplied with each ride or to use a dedicated GPS navigation device like a Garmin.