Wooden furniture is some of the easiest to maintain. The vast majority of it is treated with a varnish that helps it to resist water damage, which is vital for keeping it in good shape in most environments. That varnish may need to be replaced if it shows signs of damage, but that is fairly rare.
In most cases, you will only need to remove cushions or other textiles and then wash it with soapy water. Be careful to rinse all of the soap off with clean water after you finish. You should also be careful to avoid leaving the furniture out when the weather starts to get cold. Ice can do terrible things to wood, so it is best to take all of it into the house during winter, just to be on the safe side.
Wicker is similar to wood, but it is made from many pieces that are woven together rather from large planks. In most cases, you can simply remove all of the cushions and apply a pressure washer to blast the dirt off of the furniture. If any remains in place, you can use a sponge and some cold, soapy water to get rid of it.
Once the wicker is dry, you should apply a layer of paste wax to keep it looking attractive. Unlike wooden furniture, you can keep wicker outside during the winter, but you should make a point of keeping it covered to prevent damage. If it has cushions, take those off and keep them indoors even if you end up leaving the rest of the furniture outside.
Plastic is very easy to maintain, which is one of its primary advantages over other materials. You can simply wash it with some clean water whenever it gets dirty, and let it dry on its own over time. It is more prone to scuffing than some other materials, but those are fairly easy to fix. Simply apply a mild abrasive and rub the scuff away.
Mildew can also be a problem with plastic furntiure. You can make your own cleaner to remove it. Mix two cups of your usual detergent with one cup of bleach and dilute it in a gallon of water. Apply that mixture to the mildew and scrub it off. Be sure to do this in an area with good ventilation and wear eye protection to avoid accidents with the bleach in the mix.
You can clean metal furniture with a gentle soap and some warm water, but rust is the real enemy that you need to defeat. Some modern furniture is already treated to resist rust, either because it uses an alloy that can resist it or because it has an external coating. If yours is not resistant to rust, you should apply a coat of phosphoric acid, which is often sold as naval jelly. That will help to make sure that it does not develop rust or start to corrode, even when it is exposed to a harsh environment. It can also be used to remove rust that has already built up on the furniture. Liquid and jelly forms are available, but the jelly will usually work best with furniture.
Textiles need to be cleaned separately from frames. Hammocks and other fabrics can simply be cleaned in a washing machine. Cushions should be cleaned with soap, water, and a sponge. They need to be thoroughly dried after cleaning to prevent mildew from growing on them. It can be removed with a bleach solution if it does develop, but it is best to make sure that they are always as dry as possible.