You can dry most of the plants that you feed fresh. The exceptions would be really fleshy leaves like purslane. But clover, dandelions, sow thistles, willow, mulberry, raspberry and blackberry canes... all that kind of thing dries quite well.
Things like willow and the berry canes can be made into small bunches and hung up. Smaller individual leaves dry nicely in the kind of mesh bags that oranges or onions are sold in. The main danger is the plants may get mouldy before they dry, so don't pack them too tightly and put them in an airy, dry, warm spot out of direct sunlight. Once they are totally dry you can store them in burlap bags, bushel baskets covered with burlap or sheeting or simply leave them in their bunches and mesh bags.
If you live in an extremely humid area, you will have to guard against mould even more diligently. A fan in your drying area may be a help.
Edited to add: Plants that you are drying as medicinals should probably be labelled, just as a precaution.