Dwarf spheroidals would form in the process of galaxy/structure formation. In this process, it's really dark matter that drives growth, and ordinary matter is just along for the ride. In the early universe the dark matter is diffusely spread throughout the universe, with slight overdensities in various places. These then collapse under their own gravity and form sheets, then filaments, then finally fragment into different clusters. This would produce dark matter haloes of a variety of sizes, some of which would be dwarf spheroidals. I should note that there are problems with this picture --- the predicted distribution of dark matter halo masses does not match the observed distribution. In particular, standard galaxy formation theory predicts far more dwarf spheroidals than are actually observed.

In the case of globular clusters, the cluster would form independently of dark matter. Just as in an open cluster in the galaxy, you would perhaps have some sort of a gaseous cloud of ordinary matter (mostly hydrogen), which would collapse, fragment, and form stars. There are lots of open questions about how globular clusters form, though, so this is just a very vague sketch.