Succumb is relatively rare in spoken usage, but an example would be, "in the end John succumbed to his illness." It's a fancy word that comes to English via French and Latin and is seen most often in written English.
To give in is common in speech, examples :
She gave in to temptation.
OK, I give. (you can have your way)
Mom gave in and bought us candy.
Submit has a connotation of unequal power, examples:
You must submit to the law.
The weaker wrestler had to submit.
But submit is also used to mean "offer for a decision", like this :
I submitted my job application.