The ways in which cells move differ between eukaryotes and prokaryotes. For eukaryotes, most mechanisms seem to involve protein tubules or filaments sliding past one another and generating force. However, how such force is generated is not well understood, but adhesion molecules including integrins are involved.
See Adhesion molecules, Axon pathway selection, Cell migration, Eukaryote cell (or organism), Filopodia, Flagella, Integrins, Lamillipodia, Motility, Myosin, Prokaryote cell (or organism), Proteins