How does a Plasmodium move?
Short answer: Only some stages of plasmodium are motile.  These use "gliding motility".

Gliding motility relies on actin filaments, which enable the organism to deform it's shape, facilitating movement.  

This video provides a good visual representation of the filament-based motility.


  "Gametocytes develop into gametes in the insect midgut, and then fertilize each other to form motile zygotes, which escape the gut."




The ookinete and sporozoite are motile.  The merozoite is non-motile. 

Then of course there is the circulatory system of the host.

Source:

https://en.wikipedia.org/wiki/Plasmodium
http://www.sciencedirect.com/science/article/pii/S0092867400812817