Write down all of your verse lyrics. It doesn't matter if they're finished or still a work in progress. By writing them down, you can more easily identify a lyrical progression. Typically your verse lyrics will set the scene for the song. For example, in the song "Brown Sugar," by D'Angelo the verse lyrics start with "Let me tell you 'bout this girl, maybe I shouldn't, I met her in Philly and her name was Brown Sugar." These lyrics indicate that D'Angelo has a story to tell, but he's hesitant for some reason.
Write down your chorus lyrics. Save the "pay-off" lyrics for the chorus and use it to deliver the song's message. Using the "Brown Sugar" example again, the chorus lyrics throw aside the initial hesitancy as D'Angelo reveals his desire for the girl. "I want some of your brown sugar," he repeats wistfully. You don't need as many lyrics for your chorus. Repeat the main line to emphasize it.
Sing the first three lines from the verse lyrics. If you have an idea for a melody, use that. If not, break the words up into syllables. For example "I was wai-ting for my bu-ddy at the sta-tion." By working the lyrics into a rhythm, you can develop a melodic structure by assigning a different pitch to each syllable. Conversely, if you have a complete melody but incomplete lyrics, let the rhythm of the melody guide your choice of words.
Construct a verse melody. Using your preferred instrument and play the syllables, using no more than four different pitches to begin with. So if your opening line has 12 syllables, play twelve notes using four different pitches.
Construct a chorus melody. Use the same process, but the make this melody more repetitive. Once you have the basis of a melody that you like, experiment by adding one or two notes to create variety.
Edit your lyrics. Now that you have a melody for verse and chorus, your original lyrics may not fit. Go through each line and sing the correct melody. If a lyric is too long for the melody, use an alternate word. For example, if you're struggling to fit "garden" onto the end of a line, swap it for a one-syllable synonym, or other word that conveys a similar meaning, such as "yard." If a word is too short to fit, you can add syllables to make it fit. For example, in "I Kissed A Girl," Katy Perry sings the line "I liked it," but she makes "it" last for two syllables by breaking it up.