You first need to set up an html Form with a text input where the user submits the name
See this for Form syntax: http://www.htmlhelp.com/reference/html40/forms/form.html
You then substitute the value submitted as a variable in the query string
$user_in = $_POST['usr'];
$query = mysql_query( "SELECT * FROM phpbuilder_users WHERE username = ' " . $user_in . " ' " );
Start with the input form, post here for help with it.
Here is the input form I use
<p><form method="post" action="<?=$_SERVER['PHP_SELF']?>">
User: <input type="text" name="usr" size="10" /><br />
Password: <input type="password" name="pwd" SIZE="10" /><br />
<input type="submit" value="Log in" />
</form></p>
If the user has not yet logged in, my first page offers this and also accepts the input back: that's the <?=$_SERVER['PHP_SELF']?> bit. For the moment, you could try just posting to a seperate page that can then echo the input so you know the form works. Substitute the correct address in the action= part.
<p><form method="post" action="http://your.domain/yoursite/check_login.php">
User: <input type="text" name="usr" size="10" /><br />
Password: <input type="password" name="pwd" size="10" /><br />
<input type="submit" value="Log in" />
</form></p>