There are two versions of the answer, here: how to do what you asked, and how to do what you actually want. Chances are you don't actually want to do it the way you asked, because passing the password in the URL field is a super-bad idea. To answer the question as asked, it goes like this:
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To read the values out of the URL string, you can use the $_GET array. To print what logon is passed, do:
echo($_REQUEST[logon]);
To submit the data in the first place, you'll need to use a form. There are other methods, but this is the most basic. Something like this:
<form action="logon.php" method="get">
<input name="logon">
<input name="password">
<input type=submit value="Login">
</form>
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That being said, better practice would be to pass the password through the POST parameter, which at least isn't visible in the addressbar. To do this, simply substitute:
<form action="logon.php" method="post">
<input name="logon">
<input name="password">
<input type=submit value="Login">
</form>