Wheelbase
The vehicles are intended for off-road use. Find some large, off-road wheels from a jeep or similar vehicle. Ideally, find a set that has partial axles, instead of axles that go across the whole base. Build a small wheelbase that connects the sets of wheels, make it roughly square. Some sets also come with shock absorbers, which are perfect for the vehicle.
Chassis
Build the base of the vehicle, making sure there are two seats for the passengers in the front. Also add a turret using one of the 4-stud-by-4-stud rotating bricks. Use gray bricks for the lower half of the vehicle, as you begin to build the exterior of the vehicle. At the front, place a pair of hinges for the nose of the vehicle.
Turret
The turret is where a soldier stands and fires from behind a shield. You can make the base of the turret out of a large hinge, and then add guns made from either posts or Technic bricks. Under Resources 2, there are a images of two or three kinds of guns that can be attached to a Warthog turret. Attach this turret to the rotating piece you added in Step 2.
Nose
Use one of the trapezoidal plates to build the front of the vehicle. The vehicle also needs a winch and the namesake tusks on the front. There are a number of pieces that will work for this, like the tusks from a Bionicle set or white horns set at 90-degree angles. Place these just under the short end on the front of the trapezoid. Attach the nose to the hinges placed in Step 2, and place it at about a 30 degree angle.
Finishing Touches
Attach the windshield to the front of the car; ideally find a low and flat one that matches the contour of the nose. Over the windshield, and behind the seats, the Warthog needs a connected set of roll bars and a pair of roof lamps. No vehicle would be complete without a set of headlights as well, and a vertical vent just in front of the driver's seat.