Some songwriters can write songs without learning too much music theory or ear training. Personally, I’ve found that working on these skills have helped me in many ways. I can easily recognize the aspects of songs that I love and use them in my writing, especially when it comes to rhythms and chord progressions.
This website is incredible for interactive theory and ear training. You can go to Teoria and practice a little bit, every day, and you will find yourself improving in no time. It is also a reference for anything you might come across and need to look up.
MusicTheory.net is also interactive and set up in lessons. You can start from your level and work your way through, doing lessons and exercises as you go. There are also exercises for identifying notes on the piano and guitar, as well as general ear training.
If you’re more of a paper-and-pencil type of learner, check out the exercises on Making Music Fun. You can download these as PDFs and they’re mostly free. Using one of the websites above, you can quickly work through the handouts—practice makes you faster, after all.
This is a great resource for anyone who plays guitar and is having trouble learning music theory on the piano. There are songwriting tips as well. Everything you need is free in colour-coded and instructive tutorials.
If you prefer a blog-style approach, check out the inspiration page on the LANDR blog. They have a great way of being able to apply the theory and ear training you are learning. They make the connection from theory to song.