Look at the key of your song. This can be determined by looking at the far-left of the staff. Keys are identified by the amount of "Sharps" or "Flats" a song has. If you cannot tell the key of your song by looking at the staff, you will need to consult a key chart. For the sake of explanation, assume that your song is in the key of C -- no sharps or flats.
Determine what key you want your song to be in. Say you want your song to be in the key of G. Transpositions are measured in "steps" and "half-steps". G is 5 half-steps down from C if you were performing with a piano accompaniment.
Write a C scale. It will look like this: C-D-E-F-G-A-B-C. Assign each note a number. This will look like this: 1-2-3-4-5-6-7-8.
Write a G scale. It should look like this: G-A-B-C-D-E-F#-G. Assign each note a number. 1-2-3-4-5-6-7-8.
Look at the chords in your song. Assign each chord a number based off of the note that can be found in your scale. In this case, a C chord would be 1, and an F chord would be 4.
Write what chord each number corresponds to in the G scale. If your song in its original key goes C-F-G, or 1-4-5, then your song will now go G-C-D. This method works going from any key, to any key.