Position a ladder at one end of the aluminum gutter and climb up so that you can reach the gutter.
Insert a hand spade or small trowel into the gutter and remove any leaves, twigs and debris that is located inside the gutter.
Climb down the ladder and turn on a garden hose with a sprayer attachment. Climb back up the ladder and spray down the interior of the gutter so that any remaining dirt runs out the downspouts. Spray the exterior of the gutters as well, to remove any loose dirt. Climb down the ladder when you are done.
Pour 1 gallon of hot water into a bucket and add 1 to 2 tbsp. of dish soap. If the ladder has a safe location to hang the bucket, climb up the ladder with the bucket. If not, simply soak the brush in the soap solution and take the brush with you up the ladder.
Scrub the exterior of the gutter with the scrub brush to remove all traces of dirt from it. Rinse the brush in the soap solution as needed and move the ladder along the gutter until you have washed the entire aluminum gutter system.
Aim the garden hose sprayer at the aluminum gutters and spray them thoroughly with water to rinse away all of the soap residue.