In 1854 the U.S attempted to buy Cuba from Spain. Spain stated that they'd rather see Cuba sink into the ocean. This quarrel Cuba and America which would eventually lead to misfortune in the future and this was only the beginning of their bad blood.
Jose Marti was a poet and journalist who devoted his whole life to hoping one day Cuba will be free. He used guerrilla tactics to provoke the U.S by burning down American owned mills,plantations, etc. By doing this he only added salt to the wound which caused Cuba's relationship with the U.S to decline even further.
The U.S. newspapers did some shady things to start a war with Spain such as blaming the faulty explosion of the U.S.S Maine which killed 260 American citizens on the Spanish.
As tension builds between the U.S. and Spain it finally reaches a breaking point on April 20th, 1898 when the U.S declares war. The most famous of all units fighting in Cuba called the Rough Riders was under the command of Theodore Roosevelt and Leonard Wood.
U.S and Spain call for a cease fire and on August 12, 1898 and a treaty is signed on December 10, 1898 in Paris, France. Under this treaty Spain frees Cuba and sells Guam, Puerto Rico, and the Philippines to the U.S.
People speculate whether or not the U.S had the right to annex the Philippines. Americans felt that the treaty violated the Declaration of Independence due to the U.S denying their newly acquired territories self government.