To craft the handle bars:


To craft the axles:


To craft the wheels:


To craft the body:





Now that you have all the parts, you can craft an ATV.

To craft the Tier 1 ATV:


To craft the Tier 2 ATV:


To craft the Tier 3 ATV:


Now you have an ATV. Right click the ground with the ATV in your hand to place it down. You can get on the ATV by right clicking it. Drive forward with W and reverse with S. Steering is done with the mouse. To get off the ATV press the sneak button (left shift).

Installation:
This is a forge mod. Go to the Minecraft Forge Website
and download the installer for the recommended version of Forge. Make
sure you run Minecraft with the correct version at least once before
installing Forge. Run the installer and choose client. When finished,
launch Minecraft. Create a new profile and choose the Forge version you
installed where it says "version". Run Minecraft again using this
profile. There will be a mods folder in your ".minecraft" directory
after this. Put the ATV mod in the mods folder. Next time you run
Minecraft with Forge, the mod will be running.

License:
This document (The ATV Mod) is Copyright ©(2014)(Droog71) and is the
intellectual property of the author. It may be not be reproduced under
any circumstances except for personal, private use as long as it remains
in its unaltered, unedited form. It may not be placed on any web site
or otherwise distributed publicly without advance written permission.
Use of this mod on any other website or as a part of any public display
is strictly prohibited, and a violation of copyright.

Source:
I don't have the source code for this mod anymore. If you'd like to look at the code, you'll have to decompile the .jar file.