I'd love to.

This is the basic way to accept an invitation to do something. Here's an example:

A: Would you like to join me for dinner?

B: I'd love to.

This phrase is a pretty traditional and slightly formal answer. A more casual (and less serious) answer would be:

Yeah, sure.

Another answer that falls somewhere between "I'd love to" and "Sure" is:

That would be great.

This phrase appears in these lessons: