INTRODUCE TWO PEOPLE

to introduce someone else can also be done on a formal or informal situation

an informal situation use to be easy and pleasant for example

This is my friend Sue

This is my brother, John!

 
In a formal situation can we use this expressions

May I introduce my colleague, Sue Halen?

Allow me to introduce my colleague, Sue Halen

I would like you to meet my colleague, Sue Halen.

What to say after introductions
INFORMAL
  Answer
 
Hi Su. Nice to meet you
Nice to meet you too
 
Hello Sue I am happy to meet you Lovely to meet you too
 
     
FORMAL
How do you do, Ms Halen
How do you do
 
It's a pleasure to meet you, Ms Halen
I'm very pleased to meet you too