Put on a pair of thick work gloves.
Pull out leaves, twigs or any other surface debris from the grate. Pour water into the grate from a hose. If the water drains as usual, any blockages are clean and the drain is back to working order. If the water does not drain, you must clean the drain itself.
Lift the grate off the drain. For most drains, the grate is simply rested on top of the drain or drain channel. If the drain is particularly heavy, use a pry bar to lift it up. Certain drains are affixed with bolts that must first be removed with an adjustable wrench. If your grate is welded on, call a plumber to help clean the drain.
Pull all of the reachable debris out of the drain. Pour water into the drain when it looks clean. If the water does not drain, the clog lies somewhere deeper in the drain pipe between the surface of the drain and the pipe's exit into the sewer or elsewhere on the surface. An auger might clear the clog, but it is unlikely to be long or powerful enough. For the best results, call a contracted plumber to identify the blockage and clean the drain pipe.