Determine if the organism is multiceullar and eukaryotic. A eukayrotic cell is one that has its DNA in a specific organelle called a nucleus; bacteria do not have their DNA in a nucleus, and thus are classified as prokaryotic. Additionally, all organisms in the Animal Kingdom have multiple cells, which differs them from organisms in the Protist Kingdom (which are eukaryotic but are still single-celled).
See if the cell is missing a cell wall and chloroplast. These cellular organelles are not found in animals; they are found in plants and fungi. (Fungi do not have chloroplast, but they do have a cell wall.)
Observe how the organisms obtain their food. All animals are autotrophs, which means they cannot create their own food but instead must ingest other organisms in order to subsist.