Robin returns to find these injustices being done in KLing Richard's name (although no-one beleived it) and vowed to right them. Plus, he took a dare and killed a deer in the Kings forest, which was against the law, so he was an outlaw anyway.
So Robin Hood ran around stealing from the rich and giving to the poor and trying to avoid the Sheriff of Nottingham.
In order to draw him out into the open, the Prince has an archery competition. Robin felt he had to uphold his reputation as the best archer in Nottingham, so he went. He got caught, of course, but was rescued by his faithful outlaw band before he could be hanged.
King Richard returned to the land in triumph (at least i think he won) and promptly de-outlawed Robin, and booted his errant brother. Robin then marries his true love, Maid Marion.