Respiration happens in amoeba through simple diffusion of gases. It lives in water which contains dissolved oxygen. The diffusion of gases takes place through its cell membrane. Through its thin cell membrane this oxygen diffuses into the body of amoeba and spreads into the whole body. This oxygen is used for respiration inside the Amoeba cell. The process of respiration produces carbon dioxide which diffuses out again through its thin cell membrane.

Figure to show the process of breathing (gaseous exchange) in Amoeba

It is an aerobic respiration.