How did Washington deal with treaty negotiations, since no process was spelled out
in the Constitution?

The Treaty of Amity, Commerce, and Navigation, Between His Britannic Majesty and the United States of America, commonly known as the Jay Treaty, and also as Jay's Treaty, was a 1794 treaty between the United States and Great Britain that averted war, resolved issues remaining since the Treaty of Paris of 1783 (which ended the American Revolutionary War),[1] and facilitated ten years of peaceful trade between the United States and Britain in the midst of the French Revolutionary Wars, which began in 1792.[2] The Treaty was designed by Alexander Hamilton and supported by President George Washington. It angered France and bitterly divided Americans. It inflamed the new growth of two opposing parties in every state, the pro-Treaty Federalists and the anti-Treaty Jeffersonian Republicans.

Both countries had to aprove annexation.

February 1848 is when it was added. if that's what you were asking