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The Congress of the Confederation could "ascertain" and "appropriate" money from states or make "requisitions" on the States, as is stated in the Articles of Confederation:
The United States in Congress assembled shall have authority . . . to ascertain the necessary sums of money to be raised for the service of the United States, and to appropriate and apply the same for defraying the public expenses β to borrow money, or emit bills on the credit of the United States, transmitting every half-year to the respective States an account of the sums of money so borrowed or emitted β to build and equip a navy β to agree upon the number of land forces, and to make requisitions from each State for its quota, in proportion to the number of white inhabitants in such State; which requisition shall be binding, and thereupon the legislature of each State shall appoint the regimental officers, raise the men and cloath, arm and equip them in a solid- like manner, at the expense of the United States
Taxes versus requisitions kind of sounds like six one way, half dozen the other. First, note that appropriating money from the states means that Congress has no control over how those funds are raised (which imports and commodities will have excises). My understanding is also that taxing powers allow funds to be raised for whatever reasons a legislature might choose (i.e., the tax revenue isn't earmarked before collection). In a booming economy, revenue goes up and the legislature can choose to spend more. "Requisition power" makes it clear that the Congress only has the ability to demand funds from the states up to the amount required to fulfill its duties. Also, requisition leaves open the possibility of payments in kind (as you can see in the proposed amendment below, that says states may "pay or furnish" requisitions).
Of course, the states often ignored the Congress's requisitions, so it's debatable how much "requisition power" the Congress actually had. Proposed amendments to the Articles focused on how to get states to pay:
Art. 15. That the respective States may be induced to perform the several duties mutually and solemnly agreed to be performed by their federal Compact, and to prevent unreasonable delays in any State in furnishing her just proportion of the common Charges of the Union when called upon, and those essential evils which have heretofore often arisen to the Confederacy from such delays, it is agreed that whenever a requisition shall be made by Congress upon the several States on the principles of the Confederation for their quotas of the common charges or land forces of the Union Congress shall fix the proper periods when the States shall pass Legislative Acts complying therewith and give full and compleat effect to the same and if any State shall neglect, seasonably to pass such Acts such State shall be charged with an additional sum to her quota called for from the time she may be required to pay or furnish the same, which additional sum or charge shall be at the rate of ten per Cent pr. annum on her said Quota, and if the requisition shall be for Land forces, and any State shall neglect to furnish her quota in time the average expence of such quota shall be ascertained by Congress, and such State shall be charged therewith, or with the average expence of what she may be deficient and in addition thereto from the time her forces were required to be ready to act in the field with a farther sum which sum shall be at the rate of twelve per Cent per Annum on the amount of such expences.
Upvote:2
For the most part they borrowed the money. A lot of the money was borrowed from France and Holland who were both eager to make trouble for the British. For example, in June of 1787 John Adams borrowed 1 million guilders from Holland on behalf of the Congress. The congress also issued a lot of domestic debt, notably bonds they called "loan-office certificates." The army was largely disbanded after the British surrender in the Battle of Yorktown in 1781 and by 1784 was a small force. The major expense for the country was the interest on the debt. For example, in 1787 military expenses were $176,000 and interest on the debt was $871,000.
Another source of income was sales of land from the western territories to pioneers.
They also "requisitioned" money from the several states. For example, here is the list of assessments from 1787:
Of course, in many cases the states did not pay, or paid only a portion of what the Congress docked them.