How do you write lyrics when writing a song?

What are lyrics if not a poem? Start there. Write a poem then pick some prominent lines and repeat them for a chorus. If you can write poetry, you can write lyrics. If you are stronger at free verse like I am, some kind of structured rhythm pattern in your poem/lyrics is going to be where you will struggle but it's really not as necessary (or difficult) as you might think.

Read books about songwriting. Songwriting is an art itself. You need to know how to structure your song. I find that the most import thing in writing songs is to use poetice compoments such as metaphors, similes, e.t.c. E.g My lady's love is shaped like the ocean.

I am not a pro but as far as I know, song writing is all about focusing on a subject (it can be yourself too) and writing thing to describe about it. It need not be rhyming but if you try and make a rhyme scheme it will be easy to put it into a tune and make a great song out of it. It is basically poetry writing, but in great depth.