Mark the direction you want your trench to travel away from the aluminum gutter downspout. Spray paint works well for this. Paint a line along where you intend to dig your trench, and make sure you end your trench where you will dig your drain basin.
Dig the trench. Use a shovel to dig along the line you have painted. Make sure you make your trench at least 12 inches deep to prevent your gutter drain from rising up and out of the soil. Consider piling the displaced soil on a plastic tarp to make filling in the trench easier later.
Dig your drain basin. Your drain basin will be in the location where your gutter trench terminates. This will be where water will be deposited from your house gutter system. Your basin should be at least 16 inches deep and 36 inches in diameter. Line the bottom with gravel or pond stones.
Lay out your PVC pipe from the gutter downspout to your drain basin. Dry fit the pieces together with their couplers before cementing them to ensure everything fits properly. Once you are sure you have the necessary pieces and connections, connect them and lay your drain in your trench.
Attach a piece of perforated PVC to the end of the drain so that it lies in your drain basin. Fill the drain basin with gravel or pond stones until the pipe is covered.
Attach the end of your drain to your gutter downspout using a PVC drain adapter or rubber coupler. Test the fitting and drain for leaks using a garden hose directed down your downspout.
Fill in your trench with the displaced soil.