What are GPX files and what are they used for?
GPX files are simple XML files which contain a plotted route, track and or Waypoints or Points of Interest. These files are formatted in a way that most GPS devices and navigation apps can use them. These files are a commonly accepted standard used by many GPS vendors including Garmin, Tomtom and Trailtech. But many smartphone apps can read GPX files as well.
Loading GPX files onto a GPS device
The tracks and routes provided on this website should be compatible with most modern TomTom, Trailtech and Garmin devices. Any brand should work really - Including built-in units in vehicles.
I have no direct experience with any of them though so how that works... Not sure, but it'll probably involve the SD card that goes into the device. Check the manufacturers manual for details.
Getting GPX files onto your mobile phone
There are several ways and none are particularly difficult. Some are faster or simply better than others. Choose which method works best for you. I prefer to use cloud storage.
Using cloud storage
I use a cloud service for this. You can do this with Google Drive, Dropbox, Nextcloud or any other cloud storage tool that has an app for your phone. This works on both Android and iOS.
On Android you can often browse the cloud storage from the navigation app you are using and import the file directly. On iOS it's usually the other way around where you navigate the cloud storage app and share the file to the navigation app.
Transfer via cable
For Android, another way is to hook up your phone to your computer with a cable and use a file browser like Android File Transfer (MacOS) or Windows Explorer to put the files directly into the right folder.
If you do not know where your navigation app stores its tracks simply put the file in the Downloads folder or some generic location and import it from within the navigation app.
Memory card / USB thumb-drive
Some phones let you easily remove the SD card or even connect a thumb-drive through the charge port. Removing the SD card and loading the GPX files onto there from your computer will work as well.
In a similar fashion you can load the files onto a thumb-drive and connect that to your phones USB/charge port, you can then import the GPX files into your navigation app.
Email attachment
As a last resort you can also email the file to yourself, I think this is a silly method that works counterintuitive, but whatever works best for you of-course. From the email simply tap the attachment and either store it locally to the Downloads folder so you can import the file from there or open it in the navigation app through the choice menu.