How to apply Thevenin's Theorem to this circuit?
You have correctly calculated the thevenin resistance. Next you need to calculate the thevenin voltage source. This can be done by replacing the source in the circuit while leaving the load out, and solving for the open-circuit voltage across the load nodes.

Adding the source back in, you can find the current from the source by dividing the voltage by the simplified resistance seen by the source.



From there, simplifying the four 2ohm resistors to a single 2 ohm resistor will leave you with a single loop carrying the current you calculated. Calculating the voltage drops over each resistor in the loop will give you the voltage across the load nodes, which is your thevenin open-circuit voltage. 



Finally, you can re-draw everything as a thevenin equivalent circuit with a single source, and a single resistance in series with your load. Solving the load voltage and current should then be simple.