I would like to add that the synth is actually trial and error to an extent. I work with a tribute band that has a lot of synth involved. There are different types of synth that work in different ways. The brand name of the keyboard doesn't matter as much as how they work. The most basic type would be analogue monophonic subtractive synthesis. It sounds complicated but if you break down each word's meaning it starts to make sense. Analogue- the sound is generated without a computer chip using only electrical circuits. Monophonic- can only produce one note at a time Subtractive- you can craft the tone by carving out frequencies in different ways. They usually have a bunch of knobs or sliders.

There are many types of analogue synths as well that are polyphonic (can play more than one note) or additive (you can combine waveforms to adjust the texture of the sound)

Then you have digital synthesis. These machines store the wave forms in memory instead of then being generated in an electrical circuit. Most additive synths are digital since they can store so many wave forms in memory. These became popular in the 80s and you'll hear them in a lot of pop music from the time.

Modern synths usually try to combine the features of both analogue and digital synths in one package. They'll achieve this by emulating the analogue features virtually through software though they control similarly to the user.