What is your process?

I'm writing down an abbreviated process at www.makesomething.app -- check it out, hope it's helpful for you.

If you have any specific questions, I'd be happy to help

My process varies a lot per project and I'm still perfecting it, but there's one thing you definitely need to do (and if you've been lurking here for a while you'll probably already know it): validate validate validate.

When I built my first product I went straight into coding phase and when I finished, a year after, no one really cared about it. A few projects later, when starting to build Sitesauce, I made sure what I was solving was a real problem (talking to people, showing a MVP around, etc).

Other than that, I'd say, how you build your stuff doesn't really matter because you'll have a really high chance to succeed :D

An iterative process is important. Building on @m1guelpf and @Andremoniz 's comments it's good to authentically understand the problem (or pain) your software is going to cure but also to continue understanding it and iterate your solution in small steps. If you've heard the term 'Minimum Viable Product', start with that. Deliver the solution to the people that you're interviewing to continue to validate that it meets their needs and solves that problem.

As an additional question, is it wise to try to solve problems you (the developer) experiences and wants solved or are we likely to build solutions that fit our way of thinking and not a wider audience?

Before starting to code I try to understand if I know the customer really well and their pain. If that's not the case (or even if it is) I try to interview some potential customers for some weeks before starting to code anything. Analyse and focus on their pain.
Then I try to imagine the core features that are needed to make that pain disappear and start to code if I realize it's not going to to take me ages to build it.
I try to only build stuff that I can test it in the market at least 2 months after starting developing it