Unfortunately this little guy wasn't alive - he was dead, stained, and preserved between two glass plates. But he was frozen in a nice amoeba-ishy shape.
Amoeba moves around with pseudopods (meaning "false feet") which are really just extensions of the cytoplasm (the gooey inside of a cell). Amoeba uses its "feet" to eat too. It wraps them around some food item (usually another cell) and engulfs it. The food is now contained within a little bubble (vacuole) inside the amoeba, and can be digested.