"I see" and "I understand" can be used interchangeably when someone is showing you how to do something or explaining something.
A: "When you push the red button, you also have to push the blue button."
B: "Oh, I see/understand."
A: "When you yell at your sister, she feels sad."
B: "I see/understand what you mean." or "I see/understand what you're saying."
You cannot use "I know" in these situations UNLESS you want to make it clear that you have not learned anything new.
A: "When you push the button, you also have to push the blue button."
B: "I know, Sue explained it to me yesterday."