After a 3x3x3 method, the next step for most people is the Ortega method. First, solve one face intuitively; don't worry about solving a layer, because the face will be permuted later. Second, orient the opposite face, using the same OLL algorithms as on 3x3x3 (or more efficient ones if you want - see algs below). Finally you permute both layers at the same time (PBL). The last step sounds difficult but there are only 5 possible cases, so it is quick to learn. In total, there are 12 algorithms to learn (11 without reflections).
For the first face, without colour neutrality, the average move count in HTM is a surprisingly low 3.97, and no cases require more than 5 turns. Because of this inspection is just a few seconds, advanced users benefit from that and uses the remaining inspection time to predict the OLL case, or even the whole solve.
As a 3x3x3 Method
Using Ortega as a 3x3x3 method involves first solving the corners completely, followed by insertion of the D layer edges, and 3 of the U-layer edges. The mid-layer edges are then oriented during placement of the final U-layer edge, and finally the mid-layer edges are permuted. @see rubikscube.info link below..