How to make offers in English?

Here are a few phrases you can use. Offers often begin Would you like…?

Would you like something to drink?
Would you like some coffee?
Would you like another cake?

In a more formal style, you can say Can I get…? or May I get…? Expressions like Can I offer you…? or May I offer you…? are also possible.

May I offer you something to drink?
May I bring you some coffee?
Can I help you?
May I help you with this?

Offers to do things for people often begin Would you like me to…?

Would you like me to type your letters for you?
Would you like me to make some coffee for you?

More examples are given below.

Shall I get you something to drink?
You look tired. Would you like a cup of tea?
Can I help you?
How about a coffee?
Can I do something for you?
Can I get you some juice?

Accepting the offer

Here are some phrases you can use to show your willingness to accept the offer.

Yes please. That would be nice / lovely.
Yes please. I’d like to.
That would be very kind of you.
Thank you. That would be great.

Rejecting an offer

Here are some phrases you can use.
No, thanks.
No, thank you.
It’s OK. I can do it myself.
Don’t worry, I’ll do it myself.