As rob897 mentioned, put your index.php file in a public directory at the root of the project. That should work for you if you have all the requirements installed.
Valet is very flexible in determining which of it's many drivers to use to serve an app, and will use the BasicValetDriver at the very least, which should server your php files; what you might have is a driver that has been mismatched.
You can check which driver Valet is using for your current site by running valet which from the commandline. If an incorrect driver is being used, then you can specify a LocalValetDriver.php in the root of your app to force a particular driver simply by extending that class.