How did the United States support the Allies with economic aid while staying out of the fighting during WWII?
Basically, the US was fully isolationist pretty much up until Pearl Harbor. However, FDR wanted to help the Allies in Great Britain, so the neutrality acts that were passed created loopholes that allowed him to send aid to Britain without fighting the war. The Neutrality Acts of 1935 and 1937 banned selling arms to belligerent nations (to avoid taking sides), but Britain and France hadn't gone to war yet, so FDR could still send aid to them.
In 1939, the US realized it needed to send more help, so it came up with a new Neutrality Act of 1939. This one said that belligerent nations could buy guns, but they had to pay in cash and use their own ships (to avoid naval conflict such as the Lusitania incident prior to WWI). This was called the Cash-and-Carry Policy.
After France was taken and Britain ran out of money, the US passed the Lend-Lease Act which said that the US could lend support to Britain in the form of arms or other aid without immediate payment (it wasn't really lending, since they weren't going to get any of the items back, nor were they going to get paid back).
Through all of this, the US still declared neutrality to avoid warfare, but the Axis Powers were actually fully aware of the US's unofficial alliance to Britain.
They didn't declare war simply because they didn't want to fight the US yet (divide and conquer, essentially. We were also the biggest potential threat to the Axis Powers).
Source: AP US History