To clean your gutters, use a small broom to remove the leaves and debris from the gutters. Then use your hose to flush out any remaining debris. For tough jobs, TSP, hot water and a good brush should work. Always wear gloves when doing this chore to protect your hands from sharp edges. Proceed with caution when high pressure washing, as high pressure can dent the aluminum and/or remove the paint. Just give them a light scrubbing.
If any tarnish remains, try using a metal polish, such as MAAS Metal Polish, ZAP! or FLITZ.