Carbon has four electrons in its valence shell: 2s2 (filled s orbital) and 2p2 (unfilled). By hybridizing the orbitals to sp3 there are now 4 unpaired electrons and the carbon atom can form a bond with each of them. Since bond formation lowers electron energy this gives a great energy advantage to tetravalent carbon.
Each of the four electrons around the carbon atom can pair with one from the H atom to form a very stable bond, (Carbon does this with a single electron from MANY elements which accounts for the vast variety of Organic compounds).
Other hybridization schemes are possible to give even more possibilities! (Double bonds and triple bonds)
Carbon always forms FOUR bonds.