What are you doing next Saturday? We're having some people over for a meal. Would you like to come?
Are you free next Thursday?
Are you doing anything next weekend?
Would you be interested in coming to the cinema with me tonight?
How do you fancy going out for a meal at the weekend?
I'd love to, thanks.
That's very kind of you, thanks.
That sounds lovely, thanks.
What a great idea, thanks.
That's very kind of you, but actually I'm doing something else on Saturday.
Well, I'd love to, but I'm already going out to the cinema.
I'm really sorry, but I've got something else on.
I really don't think I can – I'm supposed to be doing something else.
It's important to be polite when you decline an invitation. We normally give a reason why we can't do something and either apologize, or use words like actually or really.