There are many ways to introduce yourself and others in Spanish. Some expressions are best used in formal situations and others are more familiar in tone. Let's look at some examples of use:

Déjame presentarme. Mi nombre es...
Let me introduce myself. My name is...

Déjame presentarte a Susana.
Let me introduce you to Susan.

Te quiero presentar a un amigo.
I want to introduce you to a male friend.

Te quiero presentar a una amiga.
I want to introduce you to a female friend.

Juan, te presento a Maria.
Juan, this is Mary.

Buenos días Luis, te presento a un amigo.
Good day Luis, let me introduce you to a male friend.

Te presento a unos amigos.
Let me introduce you to some friends.

¿Te han presentado a Pedro?
Have they introduced you to Pedro?

Va a presentarme a sus amigos.
He is going to introduce me to his friends.

¿Por qué no le presentaste a Amélie?
Why didn't you introduce Amélie to him (her)?