Newsletter subscribe. Help needed

Hello everyone!

First of all, I would like to state my point; I whant to create section in my site that you submit your e-mail and it’s for signing in a newsletter.

What I whant is so that when the user types in his/her E-mail, that this goes to some sort of database that I have, like an e-mail so that when I send the newsletter, i have all the customer’s e-mails so i can send them.

So my question is: Is that the way to do it or is there a “simpler” way of acheiving this. Because I see numerous sites that have a “sign newsletter” and I am quite interested in doing this.

Thank you in advance.