Arpeggiator,filters,tone,oscillators,sine,square,triangle,sawtooth signals...etc pheww...!!?
... talking about vintage synthesizers... must have been tough using those ! You had to have minimum knowledge in physics or electronics to master these keyboards, right ?? I still wonder -on analogic polyphonic synthesizers of the eighties(for instance), such as the DX-7(Yamaha) or the OB- series from Oberheim- why were there graphics on the zone where you select sounds, and all these waveforms ... was it really necessary, for one who's supposed to be a musician (and not necessarily a physician or electronician...) ??
Actually, it's not as hard as it might seem. If you start out with a basic monophonic synthesizer, such as a Moog Rogue, Micromoog or ARP Axxe (to name a few) you can learn a lot just by fiddling around with the knobs (or sliders) and switches. With a little bit of trial and error you can learn quickly that when you flip x switch or turn y knob, it will do this or that to the sound.
To clarify something in your question, the Yamaha DX7 is not analog. It is a digital synthesizer that operates on a totally different method than, say an Oberheim OB series, etc. Even the most experienced synth players find the DX7 frustrating to work with, though you can get amazing results with enough patience.
But back on topic, once you know how each part of a synthesizer functions, you can dial in a sound that you want fairly quickly and carry on with the more important business of playing music. You may want to check out www.vintagesynth.com to read about the different synths out there, and read the discussions on the site's forum to learn more about programming and playing synthesizers. It can actually be quite fun.