For this achievement, you'll have to level up your Long Distance stat until you can start getting missions that are over 600 miles (for those of you who are using KM, I suggest switching over just until you get the achievement). You can check how long the job is by clicking on it and looking above the map route for the total distance.
From here on, it's all about driving safe and avoiding penalties. Stay in your lane, use your turn signals and make sure to keep an eye on your overall speed so you don't go over. If you're having a tough time, you can turn off traffic penalties in the options menu or turn on the speed limiter so you can't drive over the limit. I also highly recommend you save periodically in case you crash or incur a penalty as there is no repercussions for reloading prior to a penalty and you don't want to drive 500 miles just to crash and have to start over. Also keep in mind that becoming fatigued is considered a penalty so make sure to rest before the game starts letting you know you're tired.
Another thing worth mentioning is that the damage you accumulate from wear and tear does not count against this achievement. In other words, you'll likely incur 1% to 2% damage depending on the distance you drive. As long as you don't crash or damage the trailer, this damage does not count against you getting the achievement.
Once you finally get to the destination, you're free to choose any of the parking options though I'd suggest skipping it just so you don't risk damaging your load. If everything went according to plan, you'll unlock the achievement on the results screen (even though it will likely say "Excellent" instead of perfect).