It would be a covalent bond, so yes, they would be sharing electrons.
Carbon has 4 valence electrons already, so it needs 4 more electrons to fill its valence shell, (8 valence electrons), to make it more stable. Hydrogen only has 1 valence electron. Therefore, carbon would bond with 4 Hydrogen atoms, each hydrogen atom sharing 1 electron, so that hydrogen and carbon would form to make CH4.
Hope this is what you were looking for...