The skeletal system helps give structure, movement and protection to the bodies of animals with endoskeletons. It also functions in red blood cell production, storage of energy and storage of minerals. The tissue types of the skeletal system can vary from phylum to phylum; for example, there are "cartilaginous" fish such as sharks that do not have bone tissue. As most students ask about mammals, I will answer specifically about them.
Vertebrates such as mammals have skeletal systems made of a group of tissues called connective tissue. These are bone, cartilage, ligaments, and tendons. These tissues work together in the system, and work closely with other types of components such as blood and blood vessels, joints, nervous tissue, fat (adipose) tissue and muscle. Depending on what criteria you use to determine what to include in your list, your question about "how many kinds of tissues" will have different numerical answers. The types that are generally included are bone, cartilage, tendons and ligaments. See the attached links for information that might help in determining which other tissues you want to include in your list.