First off I am linking to this excellent answer by u/barton_foley on the banking system in the Soviet Union, because it addresses very well how banking, money and central planning fit together in the Soviet Union.

To add on to it: the Soviet government always had an option of printing money. For most of the Soviet period, inflation was very low, but specifically in the Civil War years and in the late Gorbachev years, this was the primary means of the Soviet government to pay for things, especially with increasing budget deficits, and it caused a massive amount of inflation both times.

In addition, in the 1921-1929 period there was an economic policy known as the New Economic Policy, which saw a "tactical retreat" in economic terms by the Bolsheviks - private trade and industry was allowed to a relatively significant extent. Private business was again allowed with a new cooperative law from 1987 on, but even in the 1929-1987 period it's a mistake to assume that everything was state-owned. Personal property was still privately-owned, and private production, if heavily circumscribed and regulated, was allowed in certain spheres. Cooperative farm workers were allowed "garden plots" which produced a significant amount of the meat, dairy, eggs, fruit and vegetables consumed in the USSR - a portion of this was paid to the state as in-kind taxes, but the remainder they could sell privately in markets. Likewise, certain trades like carpentry, shoe-making, tailors, photographers and hairdressers could operate privately.

Anyway, domestically, the Soviet government funded itself with taxes. As far as collective farms went, taxes were in-kind - meaning that a portion of the agricultural produce at harvest time belonged to the state. This amount varied over Soviet history, but at times it could be significant, with the 1931-1933 even seeing confiscation of seed corn for the next year's planting.

To a significant degree, the Soviet government funded itself also with sales taxes and turnover taxes (which are similar to a value-added tax). Turnover taxes largely functioned via the banking system in the answer I linked to, and sales taxes were obviously collected at points of sale. A significant sales tax was on alcohol. It's also worth noting in this context that "sales tax" effectively just means a mark-up beyond production costs, with the "profit" going to the government treasury.

This is pretty much how the domestic economy functioned, but international trade was important too. The USSR did rely on exports to earn "hard currency" (things like dollars and pounds) to purchase products abroad, usually things like capital goods (so for example factory machines that were advanced technologically and could not be produced domestically). In the 1930s this largely meant exporting lumber and grain (notoriously, grain exports were a factor in the 1931-1933 famine and continued while Soviets starved), but by the 1970s this largely meant oil and natural gas (ironically, by this period, exports were actually used to by grain abroad for Soviet domestic use). Gold was also mined and used for export, but in-kind bartering with other countries was also practiced (notably with friendly socialist countries in COMECON).

Hope this helps. It's an excellent question, by the way, and can be a little hard to wrap one's mind around - let me know if anything in particular needs clearing up.

Sources:

Alec Nove. An Economic History of the USSR: 1917-1991