Remove leaves, twigs, and other debris from gutter troughs (protect your hands with gloves). Loosen dirt with a stiff brush; hose all debris out of the system.
Clean a blocked downspout by spraying with a garden hose turned on full force. Or feed a snake into it and then flush all loosened debris out with a hose.
Add mesh screens to deflect leaves, twigs, and other debris over the edge of the gutter. A leaf strainer will admit water and filter out debris.