This is outside the realm of what standard notation was designed to do, so you should do whatever you need to make it clear. Describing what you want with words is totally fine. What's appropriate depends on the level of specificity you want.
If you trust your performer to make good decisions, it can be enough to specify the type of waveform and maybe hint at some of the parameters. There are also some commonly-understood names for common sounds, for example "warm pad".
If high specificity is important, then you can make a diagram of the exact knob positions. For a simple synth with relatively few parameters, you might be able to do it right in the music where each sound is used. Otherwise, you could create a legend at the beginning of the music with each sound given a name/number, and label each section of music. Definitely make the labels descriptive though, in case the person reading it doesn't have your exact hardware.
For places where you want to indicate a parameter that should be moved on the fly, do something like this: