To make it easier on you, I have provided an example of the PHP mail function. However, you are going to want to consider adding a few things such as... an input for the subject, which is always handy. Also, make your input area become a text area, I find it easier to write something that I am fully able to see vs. only being able to see a limited view of what I am currently writing.
$messageBody = $_POST['mail'];
$to = 'youremail@whateverworks.com';
mail($to, $_POST['subject'], $messageBody);
I think these are primarily the things you really need to focus on. Take into account you are able to house a fourth parameter, generally a CC, BCC, or a FROM section (in the manual, they refer to it as the 'headers' section), which could also be helpful for you unless you plan to have somebody write their name at the end of the message (probably not very good etiquette).
Now your form.. Well.. You can structure it annnyyywwaaayyy you want.. in fact.. there are multiple ways to skin a cat.. and to create a form.. Here is quick demo of a possibility of making your form a little bit better. And if you want a little bit more reasoning as to why I used an unordered list vs a table, here is a SO Question that can give you some pros and cons over what is better and so forth. My JsFiddle can also give you an idea of how to make the display of your form look... clean.
Also, look into how you want to validate your form... Do you want to do it via PHP, where it will require the user to hit the submit button before it will look through for any errors (maybe to check for a username or for an actual message, thus avoiding spam or unwanted emails) or maybe you want to try to incorporate some browser side scripting with JavaScript to automatically check for these things without even touching that submit button.
Regarding the database, I would advise validating and making sure that you are preventing SQL injections (I will not be the only person to bring this up), which will help protect your database if you plan to upload this message and keep it for a while.
There is much thought that must be placed into creating a form, whether it is the simple HTML code, all the way through MySQL or any database code you may be working with.
Last, please please please look at the manual. In fact, I learn more from the manual now then I do from looking at other people's code because it gives real, working examples to choose from. So visit this site to make your life a little bit easier.