"May I have the sugar?" - "Here you are!"
You offer someone a gift/a coin/a ticket - "Here you are!" [Even this is not needed unless you are attracting their attention]
"Not at all!" or "That's OK!"
"Thank you so much!" - "Not at all!" [rather formal]
"Thanks!" - "That's OK!" [modern colloquial]
[Or: "You're welcome!" in America, and increasingly in Britain; or just a smile of acknowledgement in both countries]
Tailored responses
Offering food: "Would you like some more cake?"; "Do have a piece of this!"; "Like some beer?"
General invitation to eat: "Help yourself!"; "Help yourselves!"
Offering a small service like a match, holding a heavy door open, lifting a suitcase: "Allow me!" [rather formal; again, just a smile is often enough response]
...and when you can say "Please"
Asking a favour: "Would you hand me that book, please?"; "Please don't make such a noise!"
Softening any imperative: "Please help yourselves!"; "Please let me go!"; "Let me go out to play! Please!"
