To begin to understand something.
何かを理解し始める。 (nanika o rikai shimeru)
"It took him a while to catch on to the new rules."
"彼は新しいルールを理解するのに少し時間がかかった。" (kare wa atarashī rūru o rikai suru no ni sukoshi jikan ga kakatta)
to record information on paper
to end a romantic relationship suddenly or unkindly
to organize or finish something neatly
to understand something that is complicated or unclear
to be so surprised that you doubt what you are seeing
to take action or start doing something