Examine your key signature. Every piece of music has sharp or flat signs at the beginning of the printed music. These notes tell you which notes are sharp or flat, which in turn tells you the notes you will likely use in determining your chords. The key of C, for instance, has no sharps or flats. The notes are C-D-E-F-G-A-B. The notes are numbered one through seven in the scale.
Listen to the sound of the music. If it has a sad, melancholy sound, try using minor chords based on the melody notes. If you hear a brighter sound, try major chords. Chords that almost sound as if they are clashing may be more advanced chords, such as diminished chords.
Look at the first melody note in the music to determine its name and position in the scale (key signature). If you are in C and the first melody note is C, try building a C major chord around the C melody note. It's helpful to keep a chord construction chart by your side as you do this. In any song, there are several chord possibilities for a melody, so it isn't always possible to find the exact chord. In C, for instance, with a starting melody note of C, you could treat the C as the root note (chord name) and build a C, but you could also treat it as the third note of the key of A minor and make it an A minor chord.
Read the first several notes of the melody and find the degree of the scale they fall in. In C, if the first three notes are C, E and G, these are the first, third and fifth notes of the C scale. This indicates you will be playing a C major chord. If there is an F instead of an E, the F is the fourth note in the C scale and may indicate a C suspended (or fourth) chord.
Examine the bass note if you have access to it. The bass note may give you some indication of the chord being played. If the bass note beneath the C is an E, you can build a C chord around the C melody note.