I am new in web design. My problem is that after submitting my contact form it takes me to my web host website.
There could be a couple of things at work here, but first, check the action attribute on the form in question. That particular attribute informs the browser where to send the data, and user, when the form is submitted.
Here is my action code:
<form name="contactformfree" method="post" action="contactform_free/free_process.php" onsubmit="return validate.check(this)">
/contactform_free/free_process.php <- try it with a leading slash in your form action="", which means: go to the top level public directory, then go down to a folder called /contactform and then go the file called free_process.php
... assuming you have all these files and folders actually working and have not made any typos...