I think as you state the question, you are interested in the common idiom "I get it" -- meaning "I understand".
It can be in reference to learning something:
"He studied the problem for 20 minutes, then suddenly shouted "Oh, I get it!'"
Or sometimes referring to whether or not you see the humor in a joke:
"I heard that joke on TV, but I just don't get it. Why is it funny?"
"Look at this cartoon in the newspaper. Do you get it?" ...
... "Yes, I get it, but I don't think it's funny."
-- or --
... "Yes, I got it, but I don't think it's funny."
Of course, "get" and "got" are also used in the sense of "retrieving" or "obtaining" something:
"Can you get some beer on your way home?" ... "Yeah, I can get it."
"Whenever my girlfriend catches cold, 3 days later I get it."
"Do you have the wedding ring??!!" ... "Don't worry! I got it ! I got it !"