Formal Introductions

All you need to introduce people informally is to give names. 

 Introducing yourself you say: 'I'm...' or 'My name's...' 
When introducing someone else you use phrases like 'This is...' or 'Meet...' 

But things are a little bit different if you are introducing people in a formal situation and trying to be very polite. Before saying 'I'm...' or 'This is...' you have to use some formal expressions. 

Introducing yourself formally you say something like this:
 - I just wanted to introduce myself. My name's...
 - I don't believe we've met before. I'm...
 - I don't think we've actually met formally yet. I'm ... 
 The formal introduction of others requires saying the following: 
- I'd like to introduce you to...
- There's someone I'd like you to meet. This is... 
- Have you met...?

There's a little more in the video below.