What I do to improve as a writer (it works for me)
1. Writing everyday. If the muse is not present, write anyway.
2. Critical honest assessment of what I do write. Accept when something sucks and try to learn from it. Recognize when something has potential and try to improve it
3. Re-write, re-write, re-write
4. Study well written songs (in any and all genres). Try to understand what makes them well written
5. Read books on songwriting (or about songwriters/musicians). Each book has something to offer.
6. Learn new instruments. Each instrument allows a different way to approach writing and provides renewed musical inspiration
7. Try to learn the accepted song structures and work with those structures. Accept that certain writing rules and/or formulas are not a bad thing
8. When and if it serves the song, ignore all rules and formulas
9. Commit. More than anything, I am very committed and highly motivated to be the best writer I can be. It is one of a select few true passions in my life (Actually I'm rather one dimensional - being a good musician and trying to be a good writing are about the only things that really motivate me
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As far as what inspires me, writing something that is good inspies me to write something better - and - writing something that is weak, inspires me to write something better.
I think any person has certain things that they are are driven to do well (inspired). It may be playing basketball, fixing cars, building furnuture - or writing - but inspiration must come from inside, a true desire to do the best we possibly can.