We can build up MO diagram for homonuclear diatomics from our combination of AOs just like we did for the hydrogen molecule. For each diatomic the diagram will be qualitatively the same. However, it is important to realize that the actually MO calculation will yield specific energies and bond lengths that are unique for each diatomic. While this is true, the general ordering of the MOs and their relative energies compared to the AOs is consistant for the 2nd row homonuclear diatomics. Thus if we know this diagram, we can answer a variety of questions regarding these molecules by simply placing the appropriate number of electrons into the diagram.
The following two diagrams are the MO diagrams for the 2nd row diatomic molecules. There are two diagrams because the order of the energy levels is slightly different for O2 and F2 than for the rest of the diatomic molecules. Note the changing in the order of the σ and π bonding orbitals from the 2p atomic orbitals.
If you'd like, here is a full-size pdf of these 2 MO diagrams..