I'm learning how to write websites in HTML and I just learned the <form> command and the different form elements you can use with it. When I set the command to MAILTO:email@example.com it opened up my computer's default mail program. I'm wondering if there's any way to have the information sent to my e-mail without using an external program.

Yes, with the mailto in the href, the client's default email software is invoked, which
exposes the target email address.

The other choice is to send a message to the webserver where cgi programming forms parameters to the sendmail api on the webserver itself. This hides all the email addresses and allows extra data to be inserted in the message.

Instead of an href with mailto, the form action is used to point at your cgi program on the websever to process all the forms data.

You can use PHP to process the form, and then send it. HTML, in and of itself does not provide a way to email form data.

Here is a basic tutorial that should get you started. http://www.thesitewizard.com/archive/feedbackphp.shtml

On the webserver, ANY programming language can be used to process CGI requests - -
pick one you like, or if you're new to CGI & programming per se, then the PHP recommendation is just great - - it's easy to learn.

Most web hosting provideres support Perl, PHP, and BASH (aka shell programming, but NOT recommended).