While doing the final R' D' R D moves, the rest of your puzzle will look scrambled. As long as you finish the full sequence for every corner, it will magically resolve itself at the very end.
For the majority of the solve, you will treat the Megaminx like a series of 3x3 faces. Use the SpeedCube Step-by-Step Guide to visualize these layers. megaminx-solver-cheat
Just like a 3x3, insert the white corners and their corresponding side edges. You can use the standard (R U R' U') "sexy move" to slot these in. While doing the final R' D' R D
Instead of a 4-point cross, start by forming a 5-point star on the white face. Align each edge with its side center color. Use the SpeedCube Step-by-Step Guide to visualize these
Continue building "tentacles" out from your solved white face. Solve the next set of faces (yellow, dark blue, red, etc.) by forming stars and inserting corners/edges. Think of each new face as a 3x3 that you are solving layer-by-layer. Phase 2: The Last Layer "Cheat Sheet"
The last layer (usually gray) is where you can't just wing it with 3x3 logic. Use these four specific steps from GANCUBE's Official Tutorial and other experts: Algorithm: F R U R' U' F'