Identify the key of the theme you wish to put chords to. The "key" of the song determines the notes that are used in the melody. Keys can be identified simply by the sharps and flats that there are in the song. For example, the key of C has no flats, so if all the notes in the theme are natural, then you know it's either in the key of C or its related minor, which is A minor. Likewise, if the melody includes an F and C sharp, then you know the song is in the key of D or B minor. Identify the note that the melody starts or finishes on to find the most likely key.
Break down the melody into its basic components. Many musicians will use "passing notes" or flourishes to make the melody more interesting for the listener. Remove any notes that aren't essential to the overall melody of the song. Notes that are only played quickly or that are out of key are unlikely to be relevant to the overall melody.
Transpose the melody onto a musical staff. Do this by plotting the notes out into bars in their relevant positions on the melody staff. The lines on the melody staff (from bottom to top) represent the notes E, G, B, D and F and the spaces represent F, A, C and E. Plot the notes of the theme onto this staff and split it up into bars.
Look at each bar individually and determine which chord is most suited to those notes. For example, if a bar includes the notes E flat and C, both of these notes are in the C minor chord, therefore this may be the most suitable chord. This is particularly likely if you have identified the key of the song as C minor. Remember, the best major chords to use are the first, fourth and fifth notes of any key, as well as the minor versions of the second, third and sixth.
Play the chord related to the dominant note if you aren't sure. In one bar, for example, there may be a long C followed by a shorter F. Although both the C and F major chords may present themselves as an option, the C note is likely to be the best chord option because it was held longer in the melody.