You need to get into Diatonic Harmony.

As a start:

A major scale has seven notes (or scale degrees), and each one of these notes has a chord built on it as follows:

Using G Major as an easy example:

I - G Major Chord / G Ionian Scale
II - A Minor Chord / A Dorian Scale
III - B Minor Chord / B Phrygian Scale
IV - C Major Chord / C Lydian Scale
V - D Major Chord / D Mixolydian Scale
VI - E Minor Chord / E Aeolian Scale
VII - F# Diminished Chord / F# Locrian Scale

So, if you used a I, IV, V progression in G (G,C,D) then you could use any scale above as they all share the same notes. You'd probably use G major because all three chords in a I,IV,V are major and the progression starts on the root chord.

If the progression were II, IV, V you might decide to use the Dorian mode instead.

A major chord uses the 1st, 3rd and 5th notes of the scale to build a major triad. A minor chord uses the 1st, b3rd and 5th. Scales, chords and arpeggios are all very closely related - a scale is the tones played in order. A chord uses scale degrees to build triads, and an arpeggio is just the notes of a chord played in scale order...

Hope that helps get you going... :D