The 4x4 has no fixed centres and no method of its own: it REDUCES to a 3x3. Build the centres, pair the edges and solve as usual — with one trap: two parity cases that don't exist on the 3x3, each with its own algorithm.
Phase 1: The centres
Group each face's centre pieces into a 2x2 block of one colour. This is the most intuitive phase and the one you mostly do by eye: turn an inner layer to bring the piece you want to the top, place it, then put the layer back. The only thing that matters is not wrecking the centres you already built.
When the phase is finished. All six faces with a solid one-colour centre block. The edges will still be a mess — that's expected, you haven't touched them yet.
You work this out rather than memorise it: bring the piece up by turning an inner layer, turn the top face to line it up, then put the layer back. What goes up one side comes down the other.
How to hold itThe block you're building on the front face; the piece you're after, on top.
You work this phase out rather than memorise it: there is no algorithm to learn.