Results from multislit optical spectroscopy of 16 H II regions and deep Ha imaging of the amorphous galaxy NGC 1569 are presented. The extinction across the main body of the galaxy, as derived from the Balmer H alpha/H beta line ratio, indicates that most of the observed extinction is taking place in our own Galaxy; the latter amounts to (A(V)) = 1.61 +/- 0.09, while the extinction due to NGC 1569 is (A(V))(intrinsic) = 0.65 +/- 0.04. The electron temperature was measured in three H II regions using the CO mi lambda 4363 line. The O/H distribution shows no gradient along the main axis of the galaxy, which is consistent with the behavior observed in other low-mass galaxies. The average metal abundance is 12 + log O/H = 8.26, with little scatter, suggesting, on one hand, that mixing mechanisms are very efficient throughout the main body of the galaxy, or, on the other, that the most recent nucleosynthetic products are hiding in a hot coronal gas phase. Up to 20% +/- 4% of the global H alpha emission originates from the faint diffuse halo component surrounding the main body of NGC 1569. We explore the possibility that runaway OB stars that are due to cluster ejection and associated with the burst of supernovae which ended similar to 5 x 10(6) yr ago could be responsible for most of the ionization of the halo gas.