@agaric If you want a nice entry point into analog, check out the Korg Volca series. You can get them used for around $100 each.
The 2 most common ways to connect things are CV/gate and midi. CV is basically sending pulses of voltage from one synth to another to sync them together at the same tempo. Midi is going to be more common with digital synths and is super versatile.
There are also some free software synths to play with and figure stuff out, but most aren't intuitive or have a bad UI