Set your ladder up against the house so it is level and firmly placed. Secure your supplies on the roof and climb up near to the damaged area.
Wrap one end of your tarpaulin around a 1- by 3-inch board twice. Lay the board onto the roof above the hole, and drape the rest of the tarp down the slope and past the hole.
Use your screw gun, decking screws and metal washers to fasten the 1-by-3 to the roof. Select an installation location that is undamaged, and place the board so the rolled side of the tarp faces downward. Install one screw every 12 inches or so. The top side should be as smooth as possible to eliminate the accumulation of rain water.
Drive the decking screws into the roofing surface as firmly as possible so no gaps remain between the wood, tarp and roof. Install one screw every 12 inches or so. Move to the other side of the hole, and roll the loose end of the tarp onto another 1-by-3. Fasten the lower board in place at a location well past the hole so there is no chance of incidental leaking.
Move to the sides of the tarp and lay 1-by-3 boards on top of them. Press the loose tarp edges between the wood and the roofing surface, and use your screw gun and decking screws to fasten them in place. The side boards should run all the way from the top strip to the bottom, without gaps. Install one screw every 6 inches or so for a tight fit.