The layer-by-layer method in 4 stages, 3 algorithms. Full course with animations and simulator: strefa-kostek.pl/en/kursy
You turn vertices: U top, L front left, R front right, B back. Capital letter = the two layers at the vertex by 1/3 of a turn clockwise when you look straight at that vertex; R' = the other way; lowercase letter (r) = the tip only; y = rotating the whole pyramid in your hands around the top vertex. The whole time: yellow face on the bottom, green at the front, red and blue at the back.
Every tip in the colours of the centre right below it.
Turn each of the 4 tips with your fingers (u l r b) until it matches the centre below it. Nothing else moves them - if needed, fix them at any moment.
Three centres of one colour on every face, yellow ones on the bottom.
Bottom vertices: L, R, B - turn each until its yellow sticker is on the bottom face (one move per vertex). Then U until the top centre matches the sides.
The whole yellow face and the bottom row of every side in one colour (view from below and from the front).
Put a free spot at the front bottom (y). The edge that fits there: yellow + the colour of the front face. Turn the top (U) until that edge is at the top back, and check where its yellow is:
R U R' yellow on the right back face L' U' L yellow on the left back face
A solved pyramid. First U until the top centre matches the sides - after that you turn the top only within algorithms.
No edge in place - look at the front left edge, where it belongs:
R' L' U' L U R belongs at the back R' U' L' U L R belongs at the front right
Two edges flipped (in place, colours swapped) - put the good edge at the back (y):
L R' L' R U' R U R'
After the cycle the edges are in place, but two may be flipped - then go straight to the flip algorithm. The wrong cycle breaks nothing: do it a second time.