Start with something you know and develop the idea into something new.
Take a set of lyrics to a song you know very well and sing it without listening to the record. Do not play an instrument while you sing, you need to be free to adapt. You may find that you start singing a different tune to the original. Grab some music paper and an instrument and write down the tune, or record it.
Leave the tune for a while, a week , ten days, what does it matter. Now you need to break the association with the original lyrics, forget them.
When you return to your tune create a new set of lyrics.
What you have done is use a song to write a song. It is a technique used by the professionals so take a tip from them.