Castro wanted help building Cuba. The U.S. didn't even want him in power so they tried (and failed) to remove him and then ignored him. Castro and Guevara then went to other Communist countries for help. The Russians agreed only if they were able to place some missles on Cuba for strategic purposes. The States freaked the fuck out and threatened the Russians with nukes of our own. No side ever pressed the button.
Thus, the Cold War more or less.

