A major third encompasses four half tones (semitones). The first two notes of "When the Saints Go Marching In" is an ascending major third, while the first two of "Swing Low, Sweet Chariot" is a descending major third. A diminished fourth is enharmonically equivalent to a major third (that is, it spans the same number of semitones). In standard tuning, the interval between the 3rd and 2nd strings (G to B, respectively) of a guitar is a major third (each of the intervals between the other pairs of consecutive strings being a perfect fourth).
A minor third spans three semitones and is called minor because it's the smaller of the two commonly occurring thirds, the other being the major third.
An augmented third is an interval of five semitones, and is produced by widening a major third by a chromatic half tone. A diminished third encompasses just two semitones, and is produced by narrowing a minor third by a chromatic semitone. It is enharmonically equivalent to a major second,