Well, it depends on which Sumerians and when. The basic units of societal organization were the individual city complexes with their associated agricultural lands and attendant villages, which in the Early Dynastic period (most of the 3rd millennium BCE, before Sargon's conquests in ~2300 BCE) were usually independently-ruled monarchies managed through a combination of palace bureaucracy and various degrees of temple-based support. Some temples seem to have played a huge role in diverse areas of administration, in particular acting as a central redistribution-compound, overseeing the collection and dissemination of food and state-issued materials (it wasn't uncommon for kings to issue their subjects periodic allotments of things like oil, cloth, or a bulk amount of grains). Occasionally, multiple cities were unified under a single expansion-minded ruler, like in the First Dynasty of Lagash, but it wasn't until Sargon's Akkadian Empire (as far as I know) that a significant portion of the entire Sumerian urban complex came under a single form of governance for a span greater than that of a single ruler (Lugal-Anne-Mundu of Adab and Lugal-Zaggisi of Umma both conquered most of Sumer in their respective eras, but Lugal-Anne-Mundu's kingdom apparently didn't survive his death and Lugal-Zaggisi was defeated and captured by Sargon at Uruk, according to Sargonic inscriptions).

In any case, the government was essentially an absolute monarchy - at least in the areas of military affairs, domestic construction projects, dynastic succession, and things of that nature - with varying degrees of supportive theocratic bureaucracy and, sometimes, "councils" of elders or prominent citizens which might make certain legal decisions.

I can provide some more detailed information later if you like. Of particular interest is the perpetually-ongoing academic debate about whether or not any Mesopotamian governments contained elements of proto-democracy (mainly focusing on the issue of the aforementioned councils, along with some matters of the selection of kings), not to mention the complicated role of religious institutions.