How do cells move?

The two main ways are pseudopod and cilium. The pseudopod is what an amoeba uses. It moves like the blob. Basicly a portion of the cell wall softens and the rest hardens and constricts. The cell material squeezes into the softened part which inflates. The rest of the cell shrinks and the cell winds up in the new location. Cilium are tiny fibers on the cell wall of paramecium for example. The fibers are shaped like corcscrews and are rotated from the base. The base is the only example of the wheel found in living things. Cells move both randomly and by reaction to environmental chemestry, tempreture and pressure. Some react to light.

yeah I was reading a paper where a cell was able to move through a maze ... which seems interesting. It mentions that it creates its own gradient which is also interesting. I wasnt sure exactly why the cell would want to move, and how it did move when it wanted to. In this case I think it would be due to constriction.

It might help to think of cell biology as like nano machinery in a chemical plant. It's got pumps, and grids with catalysts etc. A chemical "nutrient" contacting the surface of the cell causes internal chemical machinery to come into action. At the cellular level fluid viscosity is like asphault is to us. That gives the nano machinery mechanical leverage like hydraulic machinery has. So at that scale the machinery has a great deal of force. It can, for example, break apart and combine molocules using sunlight for energy to turn co2 and water into carbohydrates. If we could figure out how to do that on a large scale it would solve the world's energy problems and make a fortune.