Locate the first note of your interval, the lowest note, or the note on the left of the pair in your interval. Think of this note as "note one." In Western music, the distance between any note and the next occurrence of the same note an octave apart, up or down, is divided into 12 parts, but we use only eight of these to describe scale steps in an octave. Letters are used to designate these steps, A through G.
Consider the degrees of distance between the two notes of your interval. Since we have seven scale steps, but 12 actual notes, we have modifiers to the non-scale tones, and this is, with one exception, "minor," one tone, or one physical key, under the next scale step. The 12 intervals in an octave are thus: one (or unison), minor second, second, minor third, third, minor fourth, minor fifth, fifth, minor sixth, sixth, minor seventh, seventh and our exception, the major seventh, the key above the seventh, and below the octave.
Apply your interval to a key signature. Technically, an interval is really a measure of distance, and exists outside of key, but when combined with the key a song is in, it becomes a powerful tool for musicians. If you are playing a song in G, for example, G is considered one, C is the fourth and D is the fifth. Perhaps the singer wants to sing the song in A, so A becomes one, D is the fourth and E is the fifth. The one-four-five relationship remains constant. This is the idea behind Nashville numbering, a form of shorthand used by studio musicians, aiding the task of transposing. Typically, Roman numerals are used to denote intervals; I, IV and V for one, four and five, as an example.