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.

Absolutely.

Say "Absolutely" to express that you completely agree with what someone has said.

You can agree with someone's opinion this way.

A: I've always said that you shouldn't hire anyone who you don't feel 100% certain about.

B: Absolutely. I totally agree.

You can also agree to a request:

A: Hey, can I talk to you for a minute?

B: Absolutely.

"Absolutely" sounds even more definite than "yes". You answer "Absolutely" when you're really sure that the answer is "yes".