This comment and the parent comment was really interesting. It's made me think about my current path and somethings I have done/learned that has incrementally pushed me towards functional programming over a long window of time.
I have played with Scheme, along with a half-completed SICP read through. I have also played with Haskell, along with partial read throughs of LYAH and real-world Haskell. Those experiences, although incomplete, have been important to me as a programmer. I don't think those actually 'sold' me on FP though.
I took a detour for some time and decided to become a better programmer using OO methodologies. I used TDD, I memorised SOLID and all that. Read up on design patterns and then used them practically. All well and good. From my toying with Scheme, Haskell and associated literature, I wasn't entirely satisfied. The code I produced was always a bit, I'm not sure, but not entirely satisfiying. It looked and worked better than what I get given to review when considering freelancers for an extra pair of hands - part of that is because of PHP I think. I carried on this way for a while in any case.
In my own self-learning, I'd started looking at language design and compilers. I read some books and decided I didn't have enough mathematical skills to consume the texts. I turned to learning discrete mathematics. That was a big eye opener. As I was reading about formal logic, set theory, proofs, etc, my mind kept turning to the problem of applying this in my work. Haskell and FP came to mind too. I believe doing this helped it finally click that a functional approach can be taken successfully in most of the work I do.
Whilst I was doing this, I had a fairly simple project that, if designed correctly, could make my life easier in future projects. I took an OO approach, designed the UML, started writing tests, etc. I decided that it was over-engineered or at least it was a lot of work for what I was trying to do. I decided to take an FP approach. I had the project completed with far less code that I was happier with. In the same language. That was almost like an 'epiphany moment'. I started getting seriously interested about functional programming then. I am now starting to see the flaws and bloat in the approaches I was taking before.
I recently read Out of the Tar Pit again. I had read it before but I didn't really get it. This time it excites me and made my brain whir with ideas. Especially on how I can make these approaches compatible with the constraints of my day job.
I actually now digest as much as I can about FP. Haskell, as an important player, frequently comes up. After laying the ground work, monads make a lot more sense. Haskell as a language excites me.
In my opinion, and I am self-taught when it comes to computers so it may not be 100% applicable, here is what I did to start my transition from imperative to declarative:
a) experiment with functional programming. Not actually get it and be ok with that. Carry on down the path.
b) Read HN and note articles posted about FP
c) Continue learning about imperative programming and consume the advice from OO thought leaders. Apply it to your work.
d) Learn a bit about maths and what it actually is, especially realising it's not just rote computation and application of algorithms from school.
e) Take a functional approach instead of an OO approach within the language you are working with. I did this in PHP. Not only will it show you how FP compares, it will also show you why Haskell/OCaml/etc by way of the deficiencies for FP in your chosen languages. In PHP, the type system (arrays as your Everyman...) and inconsistent type hints, explicit closing over of variables in outer scopes and piss-poor support for modules is one. Biggest is the only way to pass a function in the function namespace is to use a a fully-qualifies string (so function name along with namespace - you get undefined constant otherwise). With Java, it might be that you cannot have stand alone functions, which would suck.
This helped a lot for me but I'm sure spending a long time learning about software down to the hardware in my spare time contributed a lot to this too.