Hammer one stake at one end of the slope in the direction where you want your drainage ditch to go. Hammer another stake at the top of the slope the same way. Tie a string between the stakes. Make sure you tie the string at an equal level from the ground on both stakes. Pull tight. Take a tape measure and a marker and make a mark on the string every 10 inches.
Dig a 5-inch-wide drainage ditch along the string with a trencher. You can rent a trencher for the week from a home improvement shop. You will need a 1 percent incline to help the water follow the drain down naturally by gravity. Dig the ditch 1 inch deeper into the ground every 10 inches along the string. Use the marker's mark to figure that out and measure the depth of the ditch using your tape measure. Use a spade to make the slope even.
Line the bottom of the ditch with landscape fabric to keep the mud away from the ditch. If the mud gets between the gravels, it will form a seal. You want the gravel to be able to let the water go through the pebbles and into the drain.
Put a layer of coarse gravel along the ditch with a shovel. Pull on the sides of the cover and wrap the landscape fabric around the gravels tightly. That will give you a tube of gravel wrapped into a landscape fabric.
Drop shovels of coarse sand over the drainage ditch and cover the sand with more landscape fabric. You can now add topsoil and sod to plant a lawn on top. The result should be invisible to the eyes.
Align a 2-inch river gravel layer at the bottom of the ditch.
Lay a 5-inch perforated plastic pipe on top of it, holes-side up.
Fill three-fourth of the ditch with round gravel. Add straw until you cover the pipe entirely. Add newspaper on top to filter the dirt that could clog the pipe's holes.