Prior to Truman's Administration the succession after the VP went through the Cabinet. Truman disliked the idea that someone who had never ran for office may become president so he asked congress to make the Speaker of the House his Successor (Remember Truman had been FDR's VP, so when Truman became President if anything would happen to him his Secretary of State would have become President since he had no VP). This lack of a VP caused some problems for Truman, for example he wanted to fly to the Potsdam Conference but his cabinet feared that if his plane went down you would have a constitutional crisis on they hands, so he had to go by ship. This lack of a VP hurt Truman till his 1948 election when he was elected with Alben Barkley as his VP.
When President Eisenhower had his Heart Attack he left his VP Richard Nixon act as his agent i.e. act as President. They was some question as to the constitutionality of this but no one wanted to push the issue.
When President Wilson had his stroke in 1920, his wife ran the Presidency till the end of his term (She had a dislike for Wilson's VP believing he did not support Wilson's League of Nations. For this she is referred to as the "first female President" for everyone in Washington knew who was running the White House and it was NOT Wilson or his VP.). One side note, the Republicans controlled the Congress at that time (Having run control in the 1918 mid-term elections) and the GOP leadership told the VP they would support him if he made an effort to take over from Edith Wilson. The VP declined, saying the country was NOT endangered.
Since Truman's time the third in line for the Presidency has been the Speaker of the House. Now in 1967 the XXV amendment was adopted. In the XXV amendment the above problems were addressed. First, if the office of the VP becomes empty, the President can appoint a VP who must be confirmed by BOTH houses of Congress (This is how Gerald Ford Became VP and than President in early 1974 and how Nelson Rockefeller became VP later in 1974.
The Second thing addressed was when a President becomes incapacitated, the procedure are simple, if the President says he is disabled, the VP will act as President. If the VP and the Majority of the Cabinet votes that the President is disabled than the VP will act as President. If the President disagree with his VP and Cabinet than Congress will decide the matter by 2/3 vote (i.e. the President is the President unless 2/3 of BOTH houses of Congress decides the President is incapacitated).
Copy of the US Constitution on Find Law
http://www.findlaw.com/casecode/constitution/The XXV Amendment on Find Law:
http://caselaw.lp.findlaw.com/data/constitution/amendment25/