Cage method, also known as the centers last method, is a 4x4 direct solving method invented by Per Kristen Fredlund. It has a layer-by-layer-like feel.
1. Solve one side on the bottom intuitively
This is by no means difficult, but requires some experience.
2. Solve the second layer edges, ignoring the centers.
This step requires only two algorithms, usually just modified versions of the 3x3 algorithms U R U' R' U' F' U F (UF to FR) and the algorithm U' L' U L U F U' F' (UF to FL) with slices AND outer layer turns. Though, through trial and error, you may figure these ones out on your own, it will be much simpler to find a solution to this step on your good friend, the internet!
3. Similarly solve the middle layer edges. Use the same algorithms for step 2, but using double layers. That is, if the algorithm has the move "u", now turn BOTH top layers in the same direction.
By now, all corners and midges that belong on the top layer should be solveable using 3x3 last layer algorithms. Only turn outer layers and slices E, M, and S. That means no "d" "r2" "(Bb)2" etc. These moves will destroy what you have solved, and this is obviously not something you want during a speedsolve.
4. Separates wing edges on the U layer from the u slice. This step is also simple and requires only (4?) algorithms. Also, while you do this step all of the edges on the first four layers should be solved.
5. This can be done in several ways. One way would be to do commutators, which is simple and intuitive, or you could learn a few algorithms to solve a few edges at a time. You might want to combine these two for certain harder cases also.
6. Last step Use the intuitive algorithm "r U' l' U r' U' l U". you can mirror this alg and use different slices but NEVER use outer layers in this step, unless you are 100 percent sure that it works.