give (or hand) things out means give to each person (e.g. They were giving out free perfume samples at the department store.)
give in means reluctantly stop fighting or arguing (e.g. My boyfriend didn’t want to go to the ballet, but he finally gave in.)
give somebody away means take the bride to the altar (e.g. My father gave me away at my wedding.)
give something away means give it to somebody else because you don’t want it any more (e.g. Did you sell your old computer? No, I give it away)
give something away means give something to somebody for free (e.g. The library was giving away old books on Friday.)
give something away means ruin a secret (e.g. My little sister gave the surprise party away by accident.)
give something back means return a borrowed thing (e.g. I have to give these skates back to Franz before his hockey game.)
give something up means stop doing it (e.g. Don’t give up. Keep trying!)
give up means stop trying (e.g. My maths homework was too difficult so I gave up.)