Copper gutters require you to use gloves when cleaning them out. This is because of the oils in your hands and the discoloration or damage they can cause. Because they scratch easy, copper gutters require you to use a plastic scoop to clean them out. These types of gutters require you to polish them in order to keep them looking nice. Combine 2 cups each of vinegar, flour and salt. This paste is applied to the surface and wiped clean.
For cast iron gutters, it's best to keep an eye on the joints and seams. Once these begin to leak you should attach new bolts with clear silicone. If you are unable to reach the joints then you may consider putting flashing tape which has a self-adhesive and can be placed over the inside of the joint.
All other gutter types are very low maintenance but simply need to be cleaned out on a monthly basis. Part of the overall maintenance is to keep the downspouts clear. These are the part attached to the gutter at the roof line and allow the water to flow out and away from the house. In order to clear out any debris from this pipe, you should run water through it. If the water does not flow easily or at all then use a plumber's snake to loosen the debris. After the debris has been cleared then you can use a garden hose to wash out any remaining sediment. Please note that if the downspout goes underground then you will have to remove the base of it before performing this task. When you replace it back to the original position then you will have to replace the joint with a new one and seal it.