Short answer: try starting with TLA+.

I'm working on this. My colleague, who is mentoring me, is the one who's finishing his PhD in software engineering. It's his guidance that has helped me so I don't have a good answer for how to teach yourself yet. We're working on a project to create specifications for Openstack and are learning a lot by working together on how formal specifications could be taught to hackers and developers with no formal mathematics training, etc.

If you want a brief introduction to the ideas try some of Leslie Lamports talks on TLA+:

https://www.youtube.com/watch?v=iCRqE59VXT0

https://www.youtube.com/watch?v=-4Yp3j_jk8Q

If they fall into the formal specification category, I've found Writing Effective Use Cases by Alistair Cockburn to be very helpful.