This is a complex question, but let's review some key points that will help you answer it successfully.
I'll start with the conflicts between Britain and the United States. Of course, the most significant conflict here is the Revolutionary War. Colonists in the thirteen colonies that would become the United States were upset by what they viewed excessive taxation by the British as well as the circumscription of their rights to colonial self-government. In 1776, these colonists declared their independence from Britain. They then fought a war to achieve it. You will want to mention elements like the Stamp Act, the Townshend Acts, the Boston Massacre, the Boston Tea Party, and the Intolerable Acts in your answer, for they all contributed to the growing (and overflowing) tensions between Britain and its soon-to-be-independent colonies.
After the US gained its independence from Britain, it wasn't long before it entered into a conflict with France. This is called the Quasi-War (or sometimes called the Pirate Wars). It was never declared a war as such, but the conflict reached its heights between 1798 and 1800. A bit before this, Britain and France had gone to war with each other. France wanted American support (after all, it supported the rebellious colonists during the Revolution), but America was not ready for another war with Britain, so US officials declined. This led to rising tensions, the XYZ affair (in which France sought a bribe and a loan from the US), and considerable French harassment of American ships. The almost-war was settled by the Convention of 1800.
The US and Spain never entered into a formal conflict in the last part of the eighteenth century, but there were certainly tensions between the two nations, especially over the port of New Orleans and commerce along the Mississippi River. As the US expanded westward, farmers on the frontier wanted to send their produce down the Mississippi, out through the port of New Orleans, and back to markets in the East. This was much faster than overland transport, so food and other products could still be relatively fresh when they got to market.
Spain, however, tended to balk at American use of the port until the two countries established a treaty in 1795. Further conflicts between Spain and the US developed over Florida, which was held by Spain after the Revolution. The US negotiated for years to purchase Florida, but that didn't happen until 1819.