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? This is the percolation phase. This time delay will help you break the association with the original lyrics so you can put them to the back of your mind.
When you return to your tune you are ready to create a new set of lyrics. Now lyric writing is a whole other posting, check back to this site for that one.
What you have done is use a song to write a song. It is a technique used by the professionals such as Paul Simon so take a tip from them.