Here are some useful phrases to make and accept invitations in English.
Invitations are often structured into three parts: asking the person if they're free, saying what the event is, then inviting the person to attend. For example:
"What are you doing next Saturday? We're having some people over for a meal. Would you like to come?"
"Have you got anything on for this evening? A couple of us are going to the pub after work if you'd like to come."
(to have something on = to have an arrangement)
Other ways to make an invitation:
"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?"
"Do you fancy coming to the cinema with us on Tuesday?"
"Would you like to join Sally and I for a bite to eat after work?"
If your invitation starts with a phrase like:
"Would you like to..."
You can reply:
"I'd love to, thanks."
"That's very kind of you, thanks."
"That sounds lovely, thanks."
If the invitation begins:
Do you fancy coming to the cinema tonight?
You can accept with:
"What a great idea, thanks."
"Sure! What's on?"
"Yeah, why not!" (this can sound a little unenthusiastic, so use it with good friends.)
"Would you like to come over for dinner on Saturday?"
"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've planned to go away that weekend."
It's important to be polite when you decline an invitation. We normally give a reason why we can't do something and say we're sorry that we can't accept the invitation.