Convoys will unlock when you unlock and are driving to the second festival site (so Outback or Surfers depending on what you choose).
To add Drivatars to your convoy, press the right stick when they are near you to beep at them. You will see the UI above them turn orange when they are added to your convoy.
Once you have at least one Drivatar in your convoy, the fastest way to do races is to use ANNA. Press down on the D-Pad to bring up the ANNA menu (or say "ANNA" if you have kinect plugged in). From here use the Dpad to select Convoy>Race. This will start a short race between you and your convoy. Finish the race to gain achievement progress.
Do this 10 times and you will get the achievement.
Notes:
- You do not have to win the races, just complete them
- Starting and then quitting a race will not work
- Sometimes you will see a message in a convoy along the lines of "Press X to race to a location". These also count toward the achievement
Updates:
- Thanks Hirsute Dave for clarifying when convoys unlock.