Put on a pair of work gloves and some boots. A clogged yard drain will usually result in a large area of standing water, so you will want to avoid wearing regular shoes.
Use a shovel or a heavy garden rake to scoop or pull the debris away from the drain cover. Discard the debris somewhere far enough away that it will not get washed into the drain area again.
Allow the water level around the drain to drop before continuing. It is helpful to be able to see what smaller debris is stuck between the grate of the drain cover.
Pull out any smaller pieces of debris caught in the drain cover. Observe the area carefully for glass or any other sharp objects that might be caught. Wear heavy work gloves when reaching into the water to clear the drain. Dispose of the debris away from the drain area.
Observe the water flow once you have cleared the drain. If water is still backing up in and around the drain, there could be a blockage in the sewer system. Call your city's sewage or utilities department if water is backing up from your unblocked drain.