The carbon in methane and other alkanes and alkyl groups are sp3 hybrid and as such have a tetrahedral geometry. Recall from general chemistry the concept of VSEPR (valence shell electron pair repulsion). With VSEPR the things or ligands or atoms or electrons (lone pairs) projecting from a central atom will repel one another. For sp3 systems like methane that have 4 hydrogens embedded in orbitals (electrons), so these four hydrogens push away from one another so they are as far away from each other as possible. The farthest distance apart they can achieve is if they were in the far 4 corners of a box. If you tied the knots of 4 balloons together you'd get a very similar geometry. All the balloons push away from one another!