Here are some phrases and expressions used for offering in English.
See also: Free-English-Study: Offering
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1. Here. Have a cookie.
2. Would you like some pie?
3. How about a glass of wine?
4. What will you have (to drink)?
5. Would you like some more cake?
6. Can I get you some milk or something?
No thank you. It looks delicious though.
Thanks, but I don't drink (alcohol).
Orange juice will be fine.
Sure. It's really good. Did you bake it yourself ?
Well, a glass of water would be okay.
For Conversation practice :
Speaking Situations : Offering
See also :
Speaking : Accepting and Refusing
Business : Offering
Textbook: Touchy Situations, Chapter 7, New Interchange 1, Chapter 12