Caring for cane and wicker furniture is not a difficult process. If the furniture is made form good quality raw material, it is a matter of wiping it clean with a cloth and dirt can be removed with a mild detergent without harming the cane or rattan.
For banana leaf, water hyacinth there is not a lot you can do to maintain it and have you furniture last very long as the products have a limited life span, especially in heavy wear and tear areas. For woven plastic furniture(PVC and HDPE) try and minimise its exposure to the sun. Although UV filters are in most cases added in the manufacturing of the materials sun will eventually wear down the product.