Choose the subject of your song parody and a song to fit it. In some cases, hearing the original song will give you the idea on what to parody; in other cases, hearing a certain phrase may inspire you to set it to music and find the song to flesh the idea out.
Decide what subject you want to cover in your parody. For example, if you are writing about Captain Kirk of "Star Trek," decide if you want to cover his leadership skills, his love for the Enterprise or his romances with every alien female who happens his way. Keep this theme consistent throughout the entire parody.
Find a copy of the original song, either a recorded version (CD, record, tape, MP3) or the original lyrics in either sheet music format or downloaded from a song lyric website.
Make up a title for your parody. It may be similar to the original title or different. If you want to use the same title, add either "with apologies to" as a subtitle or a designation such as "No. 2" to distinguish it from the original.
Study the rhyme scheme of the original song. Follow this scheme as closely as possible. Go over the song, line by line, to get a sense of the rhythm and flow of the original words, or scansion. The closer you match the original song's scansion, the easier it will be for listeners to recognize your parody.
Start writing your parody lyrics, paying attention to the scansion. Count the number of syllables in the corresponding lines of the original song and your parody. Adjust if you have too many or too few. Recite the original song's line against your lyric and vice versa to compare the scansions.
You can get inspiration for a parody by focusing on a single line of a song or changing one word in its title to a similar word, such as changing "Sad Movies" to "Bad Movies."
Review your parody lyrics to see if they say what you want them to say, then sing them to hear if they sound right.