I have a webform and a E-mail field in it Is it possible to have a confirmation mailed out to the person registering? (as in, is it possible to have the functionality also worked in?)
On your Webform settings, click on the E-mail settings tab. Then make sure you select the radio button with "Component value", select "Email", then add this component. In the next page configure the fields as you want. You also have there a template area, where you can select a custom template and add there whatever you want. You can also use tokens.
Notice that I use the SMTP Module, and I haven't tried without it, so i'm not entirely sure it will work. Best of luck!
Drupal core modules comes with the function to send email confirmation for when a user registers. It's not necessary to use a webform for this.
With the module Webform Rules you can add conditions to your webform, each can then trigger an action. There are a lot of options for posible action, since the module Rules provides most of them. There you can check for the email notification you need.