Align the tips
Turn every small tip until its three colors continue the colors of the pieces directly beneath it.
A simple Pyraminx tutorial for beginners: align the tips, solve one face, and cycle the final three edges.

Uppercase letters turn a full layer. Lowercase letters refer only to the small tip.
Turn every small tip until its three colors continue the colors of the pieces directly beneath it.
Pick one color for the base, connect its three centers, and keep that face pointing down.
Place an edge above its destination. Use the right or left insertion according to the direction it must travel.
U R U′ R′AlgorithmU′ L′ U LIdentify the direction in which the three top edges must move, then use the sequence or its mirror.
R U′ R′ U′ R U′ R′