Offers are used to say what someone is willing to do for someone else.  The other person can accept the offer or refuse it.  Offers are always in the present because they require an answer.  To make an offer, you can use the modals:  would, can, could, may, shall, and will.  After any modal the following verb must always be in the simple form.  Following are examples of offers using these modals and positive and negative responses to these offers.  Whether it is accepted or not, it is customary to thank the person for the offer.

Would you like + noun:

Examples:
Would you like something to drink?
Yes, that would be very nice.  Thank you.

Would you like a napkin?
No thank you.  I’ve already got one.

Would you like + infinitive:

Examples:
Would you like me to read you a story?
Yes, please.

Would you like to come with us to the coffee shop?
I’m sorry.  I’ve got a lot of work to do.  Maybe next time.

Can I:  [What can I, How can I]

Can I help you?
Yes, could you tell me where the bookstore is?

Can I bring something to the party?
That’s not necessary, but thank you for the offer.

What can I do for you?
You could set the table if you don’t mind.

How can I help you?
I’d like to see your winter boots, please.

I could:

I could give you the rest of the day off.
Thank you.  I appreciate that so much.

I could stay with you while you’re sick.
Thanks for the offer, but I think I’ll be okay.

May I:

May I give you some advice?
I’d appreciate that.

May I be of assistance?
No, I can handle this, but thank you.

Shall I / we:

Shall we look for your glasses?
That’s a good idea.  Thanks for your help.

Shall I call you a cab?
No thanks.  I think I’ll take the bus home.

I will:

I will bring some beer to the barbecue.
Thanks, and I’ll get us a couple steaks.

I will help with the planning.
That’s not necessary.  Everything is already done.