You're talking about some kind of link.
There are four ways to do this:
1. Simply display the email address and let them copy-and-paste. Or some version of click-on-text+display-email. I assume this isn't what you're talking about.
2. Use a link of the following form:
<a href="mailto:email@address.com">
This will use the default email program on the computer, if one exists. It will require that the user clicks "send" in that program (after typing a message).
I think this might be what you're talking about.
For more information, use a search engine to look for "mailto link". (And you can test it out in your browser right now in the URL bar.)
Honestly, this is a somewhat lazy option that most users won't find very useful or professional. Personally, for example, I don't have a default email program because I use a web-based email service.
3. Use a form and a "free form mailer" (you can search for that). That is, you will use a free service that will automatically email the contents of a web form on your page. Instructions are provided on the websites of the many different services.
This is easy, though can lack in customization (but look around for one you like) and can often come with ads for you and/or the user.
4. Create your own form mailer to send the contents of the form to your email. This is the hardest (you'll need to know something about a serverside programming language), but you can control it completely and it will have no ads and it will be very easy for your users.
You could either write all of the code yourself (consider this the "advanced" version) or search for (free or for-sale) third-party software that will do this for you (again potentially with some limitations in customization if you don't know how to modify the code).
Most importantly, you'll need to use a serverside language that is compatible with your server (and installed). In most cases for basic webhosts, that is PHP. If you search for "PHP form mailer" you'll get a lot of results to help you there, and many of us can help here too.
Personally I go with option (4), but I also already know how to use PHP. It's the "best" option, but also the hardest. So it's all up to you.
As the simplest answer, just do (2) above. It's not perfect, but it'll work sometimes, perhaps most of the time. (Depending on whether the user has/uses the default email program. Many do.)
