According to the Pauli exclusion principle, when can two electrons occupy the same orbital?

When they have the opposite spins.

The Pauli Exclusion Principle actually states that two electrons cannot occupy the same quantum state. To occupy the same quantum state, they would have the same ##n## (quantum level), ##l## (subshell), ##m_l## (orbital), and ##m_s## (spin).

In order to differ in quantum state, but be in the same orbital (same ##m_l##), you only have to have a different ##m_s##. Since ##m_s## can only be ##+1/2## or ##-1/2##, the electrons just have to be opposite spins to be in the same orbital.