Plot a direct line, pointing away from the house, from the drainage system downspout across the lawn to the spot where the drainpipe will empty out. Avoid plotting the drainpipe route where trees, large shrubs or other obstructions prevent digging a trench into the ground.
Mark the drainpipe pathway by hammering a wood stake into the ground at the downspout and at the exit point. Stretch a length of string from one stake to the other.
Remove any obstructions along the path of the string line that prevents the digging of the trench.
Use a shovel to dig a trench that is 12 inches wide and at least 8 inches deep along the string-line. Slope the trench 1/4-inch for every foot of the path taken by the drainpipe.
Spread small gravel evenly 2 inches deep along the bottom of the trench.
Lay 4-inch diameter PVC pipe from the downspout to the spot where the drainpipe exits. Ensure that the drainpipe is resting evenly on the gravel.
Brush one end of a PVC elbow joint with PVC cement, according to label directions, and fit a drain connector onto it. Drain connectors are available at home-improvement stores to fit rectangular downspout pipes on one end and different sizes of round pipes on the other end.
Spread PVC cement onto the end of the elbow joint and connect it to the 4-inch round drainpipe lying in the trench.
Dig a hole approximately 2 feet in diameter and 12 inches deep at the drainpipe exit spot. Shovel 4 inches of gravel into the hole to slow down the flow of water and maintain even drainage.
Shovel 2 inches of gravel gently over the drainpipe and cover it with dirt. Return the excavated dirt over the gravel and place sod over the dirt.