Ableton's guide and Syntorial, both mentioned elsewhere here, are great introductions. Subtractive synthesis (which is the style of synthesizer your probably have in mind implicitly when you say "analog") is fairly straightforward in practice and decomposes into separately understandable components really well. It's a good fit for programmer brains that think in terms of composing smaller units together. It's literally just oscillators, envelopes, filters, and LFOs. Everything else is secondary.
Once you get the basics down, when it comes to real sound design I've found the best tool is to get on YouTube and search for "<name> sound design" where <name> is the kind of sound you want to make: spacey pads, EDM pluck, dub techno stab, 90s synth bass, etc.
Over time, your ear will get better at hearing a sound and understanding how to build it in a synth. You'll learn to hear the difference between a sawtooth and square, what different filters sound like, and how detuning, unison, PWM, etc. all affect a sound. Tutorials are a good way to build up that knowledge.
Also, just like programming, there is absolutely no substitute for just sitting down and noodling with it yourself and trying to make sounds. Like cooking, much of the learning happens in the intuitive non-verbal part of your brain. You don't just need to learn the words for things, you need to develop a deep auditory intuition around sound. You need to feel it. Books will only get you so far with this. Making sounds yourself is key.
You can do this all on a computer using software synths if you want. You can get a free or cheap DAW like Reaper or Ableton Lite and then a free soft synth like Tytel's Helm.
But, personally, I think it's more fun and easier to learn on hardware. That lets you engage your sense of touch and muscle memory, which helps really lock in the learning. The Korg Monologue is a great analog subtractive synth to start with, or a Minilogue if you want to play chords. Hardware holds its value really well, so you can always sell it and recoup most of your investment if you lose interest.
Note that subtractive synthesis is just one way that machines can make sound (but it happens to be one of my favorites). Over time, you'll want to explore FM, wavetable, additive, granular, etc. There's a ton of fun to have.