By and large before air travel became standard the main way that Presidents got aboard was on US Navy warships. We should also note that this is actually a pretty short timeframe that we are talking about!

The first President to travel to another nation was Teddy Roosevelt in November 1906 when he visited Panama and the Canal Zone. Teddy rode the battleship USS Louisiana which was brand new at the time, and had just returned from Cuba where it had ferried Secretary of War Taft on a mission, and was conveniently at anchor at Norfolk then for the trip. As remarked upon by this blurb in a newspaper of the time several cabins were modified for the comfort and use of the Roosevelts. More about their accommodations can be found here in this PDF of the San Francisco Call; http://navsource.org/archives/01/pdf/011940s.pdf

While FDR would be the first to travel to another nation by air. He took a specially modified Pan Am Clipper to the Casablanca Conference, the idea being that it was worth the risk to avoid U-Boats all together in January of 1943. While he used a modified C-45 (with elevator for his wheelchair and all) to travel to Yalta in early 1945. However both he and Truman would travel by warship during their time in office and it would be Eisenhower who would become the first to travel by air as the go to. FDR had traveled often by sea, both before and during the war. In the 30's he took several goodwill tours of South America, one notably aboard the famed cruiser USS Indianapolis. While he would first meet Churchill in person at the Atlantic Conference in mid 1941, both leaders took warships for maximum security, Churchill the battleship HMS King George V, and Roosevelt the cruiser USS Augusta. In the summer of 1945 the same Augusta would serve as the enter piece of a convoy that took Truman to the Potsdam Conference. During stops in Britain the ship would be visited and host the King as well, while aboard all naval traditions were observed too, including the President being 'Piped' Ashore when leaving in Antwerp.

For reference the State Dept even maintains a log of every trip evry President has ever taken to another country: https://history.state.gov/departmenthistory/travels/president