How does the amoeboid movement occur? What are examples of beings and cells that use such movements for locomotion?

Amoeboid movements are formed by cytoplasmic movements and plasma membrane projections known as pseudopods. Their formation actively alters the external shape of some portions of the cell surface making it move with a substratum. Pseudopods appear from differences of viscosity between neighboring regions of cytoplasm near the plasma membrane and from the contractile action of microfilaments.

Amoeboid movements happen, for instance, in amoebas (a protozoan), organisms that use their movement to find food. The leukocytes, cells of the immune system, when involved by chemical substances (immune mediators) use amoeboid movements to get out from capillaries in regions of tissue damage to participate in the inflammatory process.

Cytoskeleton and Cell Movement - Image Diversity: pseudopods