Analyze the melody to determine the names of the notes in the melody. Find the tonic of the melody. The tonic is the note that the melody revolves around. The first and last note of a melody are usually the same. You can use the first note to create the chord for the first and last bar of the music. Simply make the first chord a major triad, by adding a major third to the tonic and then a minor third on top of the major third.
Find the chord for the second measure by looking at the melody. If the melody has a C on the first beat of this measure, then build a chord on thirds. In this case, it would be a C, E and G, which creates a C major chord.
Move between chords by choosing chords that are not adjacent to each other. For instance, don't move from a C chord to a B or D chord. When moving from one chord to the next, it is best to use a common tone between the chords. Between a C and D chord, there are no common tones. For instance, C, E, G and D, F, A don't share any notes in common. However, C, E, G and E, G, B both share two notes. This makes the move from one chord to the next smoother.
Place a V chord as the second-to-last chord to ensure that you have a proper cadence.