Should be near enough the same on a Mac.
The file comes into downloads.
Simply clicking on it should start BaseCamp automatically. The routes should then all appear. As it's a downloaded file it's sometimes necessary to check the file extension; my Mac seems to add .txt to .gpx I have no idea why. Similarly, in BaseCamp it's often necessary to change the name of the download or it get overwritten by the next download.
I thought it read he was was having trouble installing basecamp and not the actual gpx file download, i may be way off base with my reply then if its the gpx download he is having trouble with, i feel sure he will reply back if a problem persists.