Somebody asked this question on a musical synthesizer group on Facebook recently. What I have written below is more or less my reply to that question. As it seems like this could be a relevant answer that I might not want to type out again and again and have also provided in different ways before, here is my blog post on the topic.
Learning synthesis is such a broad topic with so many ways to start. The best way to start is to pick a particular method and start. For instance, let's say there are three ways to get started: 1) Buy a synth and start playing, 2) Download software, free or paid and start using it, and 3) Start building your own synths - the DIY route.
Within those three categories, you can see that there are lots of ways to go in each of them. Sometimes people are guided strictly by budget because they just do not have the money while others are drawn to a particular part of playing and making music.
I would recommend watching some YouTube videos on some current synths as well as looking up some DIY stuff. You might be intimidated by the DIY route but the great thing about it is there is actually nothing to buy. You can look at it educationally and learn about things like:
1) What is a waveform,
2) What is voltage,
3) What is current,
4) What are the different waveforms used in synthesizers,
5) What is frequency,
6) What is a filter and what are different types of filters,
7) What is an LFO
Actually, before you go about buying anything, those topics above are a great place to start learning about synthesis no matter what route you choose in the end. If you only see one video on each before you buy what you buy, do not feel guilty; you can easily learn more as you go along if that is what you want.
There are some likely options you will be recommended: 1) Buy a 1 knob per function synth or 2) Get a MIDI controller and start using a free DAW or a soft synth. Given those two options, I think the 1 knob per function synth is the better especially if the physical synth has MIDI DIN ports. This will allow you to use the synth as a MIDI controller.
I think that if you watch a number of YouTube videos on different synths as well as MIDI controllers and some basic use of DAWs, you will figure out what way you want as a starting point. Remember that there are often free pieces of software as well as paid and each of those will have videos on their use on YouTube.
Keep in mind what your budget is because it is very easy to jump right in and buy something that is beyond that budget. Buying used is an option.