• It might help to think of the game as Sokoban, except that it's on a triangular rather than rectangular grid.
  
• In addition, being able to pivot and rotate a pyramid also allows you to do stuff you cannot do in Sokoban. As a result, there are multiple ways of moving pyramids from tile to tile, and these affect other adjacent pyramids in different ways.
  
• But some rules still apply. For instance, when you directly push a pyramid, it only travels by one tile in any direction, and only to tiles connected by an edge.
  
• You can only push and rotate pyramids, but you cannot pull. So if a pyramid is in a dead end, it's typically not possible to get it out, unless e.g. there are other tiles to help, or you can make a path there, or something.
  
• Because of the triangular grid and the ability to rotate pyramids, you can sometimes affect pyramids that are only connected to yours by a vertex, rather than a whole edge.
  
• The former point also applies to pyramids affected by pyramids you push. This can sometimes look like you're pushing blocks à la Sokoban, except with empty tiles both in front and behind the pyramid you're pushing.
  
• Sometimes not all pyramids are required for the solution.

Slight spoilers on some of the game mechanics follow, but I don't touch on any particular puzzles.

Later parts introduce floating pyramids, floating platforms, and breakable platforms. Some tips for these:

• You can stand on floating pyramids, but only when there's no floor tile below them.
  
• Floating pyramids can be put on other floating pyramids. However, this is not trivial to accomplish, because pushing a pyramid onto a floater pushes the floater, too.
  
• Floating platforms can replace breakable platforms (so they're no longer breakable). But this only becomes relevant in part VI, when multiple puzzle mechanics appear at once.