The issue with describing the government of the Republic of Venice, as with any other historic Italian Republic, is that the system of government was a continuously evolving thing. The Republic in the tenth century was a very different polity than the Republic in the thirteenth century, which in turn would have been unrecognizable in the fifteenth. In fact, the system of government's only consistent characteristic can be said be its need to balance the needs and concerns of all groups within the polity.

If you're interested in the politics of the earliest days republic, this answer of mine addresses the interactions between the three main groups in the lagoon in the eighth and ninth centuries: the pro-Byzantine landowners in Eraclea, the pro-Republican merchants of Malamocco, and the pro-Frankish Clergy. This other post of mine more or less picks up where that answer left off and explains, with a bit of rambling, the dynasto-political struggles in Venice the following century.

The Venetian Republic became more oligarchic in the next two centuries, I examined the events leading up to the the implementation of a more "sealed" oligarchy and a more complex system of government in this answer, while in a post on the same thread as a pervious post, which you can access here, examines the Republic of Venice's government at its height of power.

For comparison's sake, you might be interested in this answer about the government of Republican Florence, through the lens of Cosimo Medici's ability to govern behind the scenes. This other answer you might also be interested in explains how the Medici were able to continue ruling even after the collapse of the Medici bank.

And finally, if you're interested in a broader answer looking at the roots of the Italian city-republics, this answer might be interesting to you.