Well, I would say more generally that "taxes" as we think of them operated very differently in the Middle Ages and had different uses and that is worth remembering regardless of your locale.

But onto your question. The Italian cities did not come up with an income or property tax until the early fifteenth century, and even then it was not widespread until later. Cities typically extracted funds from various forms of indirect taxation, i.e. a set sum of money for each pound (or cantera or what have you) of salt you bring into Genoese territory. This could be applied to just about any tradeable commodity.

Now, this sort of trickle of income was not enough to wage war (the primary expense of the Italian city-state, they really didn't engage in many large projects), so the cities, beginning with the Genoese, sold off shares in future profits from these taxes in exchange for cash up front to pay for fleets, fortifications, etc. This is actually a fairly sophisticated way of financing the state. For example, the Genoese public debt became so complicated that they created the Bank of St. George, which acted essentially as the Bank of England would years later. These sorts of experiments with state banking made the Genoese useful and influential in this capacity long after the city's dreams of MEditerranean empires had faded and paid for the Palazzi Rolli in that city: https://whc.unesco.org/en/list/1211/.

Edit: Just to add a source that covers all this thoroughly, Domenico Gioffre, Il debito pubblico Genovese: Inventario delle compere anteriori a San Giorgio o no consolidate nel banco (sec. XIV–XIX).