It’s been a while since I did it, but from what I recall, the VST host gives your plugin a native window handle, that you can slap whatever graphics and event handlers you want into. There’s also the “standard” VSTGUI library, which is a thin wrapper on top of this that lets you design a GUI using widgets that are “known to work,” but you could just do your own thing. Some plugins create a new OpenGL context to put inside the window, even.
Also, in VST 3, the “host interaction” part is clearly separated from the “plugin processing” part, and commands for how to change things flow as marshaled data packets across – you’re not guaranteed that your DSP code runs in the same address space as your GUI code. This makes things like in-plugin VU meters annoying to implement, but it does have the benefit that GUI interaction really is separate from the DSP, and the DSP could conceivably run on DSP cards or whatnot, and the GUI could conceivably run across a network. Maybe Yamaha uses this for their large location mixing consoles or something, who knows?