Some tree species are better suited for this style than others. Juniper and Cotoneaster are the two most popularly used to develop cascade bonsai because of their natural tendencies. Both of these species naturally grow close to the ground and are commonly used as ground cover. With a little wiring, you can easily train both of these species into cascade bonsai.
Other trees that are used to make great specimen cascade bonsai are Japanese Black and White Pines, Mountain Pine, and Scotch Pine. Pines are typically best for this style, but with some extra work, just about any species can be used. If you are ambitious and use a broadleaf species, make sure that the sun is not beaming on the undersides of the leaves.
It is best to start this process in early spring while the branches are the softest. Clean all dead wood and foliage out so you have a clean tree to work with. You may want to trim about half of the branches off of the tree. Start with the smaller branches first, then see how it looks after those are removed. After that, decide where you want the apex of the tree to end up.
Once you have that figured out, you can start wiring the truck and branches into the desired shape. You may have to double the wire to get the right amount of bend, since bending downward is not easy. Start by anchoring the wire to the trunk and then move your way up the entire trunk. With the trunk wired up tight, you can bend the tree in the desired shape.