You can obtain the ATV quest line by talking to John Harris at Embry Crossroads (he is behind the nature merchant building right next to the bank). Then complete the entire quest chain which can be found here: Building your first ATV .
The ATV requires a Coordination stat of 30 to be able to use it.
(Warning: this quest line may require some help from others, and may take a while...do not expect to solo it reliably until level 14 or 15 for most people)
Once you have completed the quest line you should have everything except the book to craft a vehicle repair kit. Once you get that from a science merchant you can craft the vehicle repair kit, then using all the parts craft the ATV. Read below for further details.
|Fuel Type:||Can of Gasoline|
|Slope Angle Limit:||600|
|Max Turn Angle:||900|
|Weight Capacity:||90.0 kg|
|Skill Req:||Coordination 35|
|Triggered By:||ATV Key|
Requires knowledge "ATV", learnable at upon completion of the ATV Vehicle quest line after acquiring the individual knowledge books Control Systems 1, Engine 1, Frame 1 & Tires 1 given throughout the quest. You will also need the Basic Vehicle Repair Kit to be able to craft the ATV. If you want to craft the repair kit, you can find the recipe at a Science Trainer. Crafting the actual ATV will require a Science skill of 30.