AFCI breaker tripping when any load attached
Proper wiring
The first step, is to inspect the breaker installation. Make sure it's installed properly, and all connections are tight.
For an AFCI breaker, the grounded (neutral) and ungrounded (hot) circuit conductors should connect to their respective terminals on the breaker. The coiled grounded (neutral) wire from the breaker, should connect to the grounded (neutral) bar in the panel.

If the circuit neutral is connected directly to the neutral bar in the panel, the breaker will trip as soon as current is drawn through the circuit.
Short-circuit
Next you'll want to check the wiring for a short. Disconnect the ungrounded (hot), and grounded (neutral) conductors from the breaker. Use a multimeter to test continuity between the ungrounded (hot) and grounded (neutral) conductors, ungrounded (hot) and grounding conductors, and grounded (neutral) and grounding conductors.  You should have no continuity between any of the wires (assuming there's no load connected).
Test the breaker
If you have a spare bit of cable left over, you could rig up an example test circuit.  Connect a short bit of cable to the breaker, and wire the load at the other end. Carefully turn the breaker on, and see if the problem persists.  If the breaker trips, try replacing the breaker (they are known to be/go bad from time to time). If the breaker holds, the problem is likely with the wiring.
Visual inspection
The last test would be to visually inspect the wiring, which I'm assuming is impossible (or quite difficult).