I personally don't like to force songwriting. I usually start off with finding things that inspire me, or make me feel extremely deep emotions. It's pretty easy for me to turn my brain off, thankfully, so I can completely zone out and write from the heart.
A rule of thumb for me with poems and songwriting has been, "Don't sit down with the intention to write, sit down because you have an idea that needs to be written down." That's something that's seriously helped me throughout my time. Also, don't get too nitpicky with lyrics as they first come out! It's so easy to just get distracted with which words you're using and how it sounds; Just write what feels natural and then work it afterwards.