Reddit mentions of Refining Sound: A Practical Guide to Synthesis and Synthesizers

I'm not the most qualified person to answer because I'm still learning the ropes myself, but I can tell you the path I took. This is just one approach:

I would say the first step is to learn a DAW (digital audio workstation). I'd recommend Ableton just because it is very popular so you will find loads of resources and online tutorials. Reaper is also a good option if you don't want to spend a lot of money.

Then you may want to learn synthesis. Start with subtractive synthesis and in the future you can learn about FM, additive, and granular synthesis. You could try Syntorial (highly recommended) or a book like Refining Sound but I'm sure there are some good free tutorials out there if you look. Pick one synth plugin you can mess around with. There are loads of free plugins but you can also try Massive, Serum, Ableton's Analog, etc. For something a lot more complex but great for ambient, you may want to learn Reaktor (I think Tim Hecker uses Reaktor in some of his music). Here's a free online course that will teach you synthesis and Reaktor.

Finally learn about effects. Check out VahallaDSP, Audio Damage, FabFilter. Ableton Suite's built-in plugins are all really great too. You'd be amazed how a good reverb can totally transform your sound. Again, there are lots of free effects plugins you can download as well.

If you want to go the hardware route (which is much more expensive but can be rewarding), I'd suggest getting a polyphonic synthesizer. The Korg Minilogue, Roland System-1, or Novation Mininova could be good places to start. Pair that with a good effects pedal (the Zoom MS-70CDR is a great and affordable multi-effects pedal) and you can start making ambient music right away.

My last and most important piece of advice is to use the internet. There is just a plethora of resources online. Just google what you want to do (e.g. "how to make drone music on ableton") and you'll find tons of youtube tutorials, walkthroughs, forum topics, etc. It may spark more creative ideas and lead you down a new rabbit hole.

EDIT: One more thing, be sure to check out /r/edmproduction. Despite the name, it's a great place to learn about electronic music production in general.

maybe look at books:

http://www.pdfhacks.com/eno/BE.pdf (PhD dissert on Eno's works

http://www.amazon.com/Refining-Sound-Practical-Synthesis-Synthesizers/dp/0199922969

http://www.synthesizer-cookbook.com/

(The Shepherd book is really good, i haven't read the cookbook but it's mentioned here regularly. the Eno book doesn't talk synthesis per se, but very interesting

One of the most comprehensive free resources is Julius O. Smith's website on mathematics of the Discrete Fourier Transform, synthesis and DSP, physical acoustic modeling, geez you name it.

A less mathematical but still good recent book on synthesis is Refining Sound by Brian K. Shepard.

check out refining sound: a practical guide to synthesis and synthesizers. i read this book when i first started.

also, apple has some good explanations in their logic documentation.

There is no significant advantage to using a dedicated hardware synthesizer over a computer. To the contrary, a computer gives you far more flexibility, and it takes up a lot less space.

Don't get me wrong, though -- I absolutely love both hardware and software. I just think you can learn a lot more about synthesis and music production with cheap or free software than you can with a single dedicated synth in the introductory price range. I would recommend buying a midi keyboard and a copy of this book. It gives recommendations of free software you can use while working through the book, and it will teach you the fundamentals (and then some) of all the major forms of synthesis.

Plus, if you buy a midi controller, you can use it to control hardware synths later on, if you choose to purchase any.