I wouldn’t create an actual file called contact.php.
Just create a Page called Contract.
Then put the ‘code’ for your contact plugin (e.g. <!--contact form-->) in that pages content.
That’s it.
Most contact form plugins include directions on doing something like that.
Codex is your friend – http://codex.wordpress.org/Pages#Creating_Your_Own_Page_Templates
Adding
<?php
/*
Template Name: Contact Page
*/
?>
at top of that contact page file that’s compatible with WP and your theme, and upload to server within your theme’s folder. Then create a page, and choose “Contact Page” on the right sidebar under “Page Template”, publish the page and you’re good to go.