The Fed issues as much dollars as needed by writing the new trillions on its balance sheet. These new trillions are channeled usually via government bond buying or through the banking system.
The US government designs its economic policies in a way that makes its trade balance of payments always negative (by large values). Therefore, trillions keep flowing overseas (to pay China, EU, Japan etc for the imported goods and services).
Moreover, the US coerces foreign governments to trade between each others in USD; especially for oil and gas. In this way, the ‘excess’ dollars keep circulating worldwide.
