Different artists write songs in different ways. I know musicians who write the melody first and add words later and later still, create a chord structure to make the song. Other musicians write the words first and then add a beat/rhythm to the words and write the melody to the beat. Some play chords and just start singing a melody and lyrics of the top of their head. Still others, write in pairs, where one person writes the music and melody and the other person writes the lyrics.
Tip: I recommend that you find Your way. Ask your self what do I have? If it is a melody start with that, if it is just words, start with that, if it is a song you play on an instrument with no words or melody, start with that. After you have written several songs, you will start to see a trend. Maybe you notice that you always start just singing melody and lyrics or you always start with the background music or the chord structure, or you start with a poem. Once you have figured out the way YOU like to write a song, the whole process will seem much more fun and less daunting because you have a starting place. You have found Your way.