Pets are wolves
To tame a wolf you have to collect bones, which you will get from skeletons. Hover over the wolf until the word 'tame' pops up and click it. It might get angry and you'll lose a bone or two but no worries just keep clicking. Do not hit it! It will attack! When the red collar appeared it's yours and it'll follow you everywhere. Make sure to check if it's sitting or standing or it might not follow you. Get more wolves by taming two adult wolves feeding them and you'll get a baby one. Beware: they follow you everywhere litterly EVERYWHERE!