I’m thinking about getting a Garmin or suchlike as I mainly cycle alone and would like to start exploring new trails. I have seen data for these trails on sites such as trailbadger.

Can you just download the data to a Garmin and then use it more or less as a sat nav to guide you around unfamiliar trails?

Yes, some GPS routes are a list of waypoints & the GPS will guide you with direction & distance from one waypoint to the next, but more modern ones will show you where you are in relation to your route that is a line on the map of the GPS.

most of these files will be GPX files and are very easy to download to your device.

if you have never used a GPS before I think its prudent to mention that they are no substitute to map and compass if you are going riding in the hills where visibility can make navigation hard!

yes you can use them to navigate but you are often doing it without a map
IME you need both with you but a GPS will help with decisions and stop you getting the map out all the time.

If you have an iPhone have a look at Trails (can pre download the area maps so you dont need a connection) or Endomondo (can hookup to a heart rate monitor) and has an excellent site for sharing and making challenges. Oh, get a heavy duty case also!