How to execute some code on button click

Hi
I am working on my very first plugin, and I am using the wordpress plugin boilerplate.
I know how to run some code on a specific event, but I don’t understand how to run some code when I click a button or a link.

Basically I want to save some options in an option page (I have done this already) and then I want to run some other code when I click on another button or link.
Or it could be handy to me enough to know how to run some code when I call a page (and then I could call that page using ajax)

can anyone point me to the right direction for that?

thanks