This definitely depends on the server you're using, but since you're a PHP MVC noobie I'll reference apache in this example, and hope it's what you have for the sake of the examples.
First, you'll need your webserver configured to know that it has to send all traffic through your base page (usually index.php). Now that page would do some other stuff (call bootstrap, etc) but for the sake of argument we'll say that all it does right away is look at the request from the page, compare it to the DB, and complete the request if it can.
In that case, it will be helpful to have the request info from the server passed in to the index.php page. To do this, you'll want to configure apache with an .htaccess file similar to:
DirectoryIndex index.php
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.+)$ public/?path=$1 [L,QSA]
This tells it to use index.php for all requests that aren't specific files or directories, and to pass the full url path through to index.php as a $_GET var.
Next, in index.php, you'll want to check the path you were passed against DB of paths. Here's a really simple example to show:
<?php
// Obviously use your database and some string parsing here to match correctly
// I generally explode the path on '/' to break it into controller, action, etc.
if ($_GET['path'] == "user/account") {
// Then you call the controller that matches the first part of the route
// The action that matches the second part of your route
// And pass the request along so you can access anything else
call UserController::accountAction($_REQUEST);
} else if ($_GET['path'] == "user/resetpassword") {
call UserController::resetPasswordAction($_REQUEST);
}
From there, you should be in the right place and have everything you need. That Controller/Action URL format is a fairly common one for how easily it lets us do this.
Hope the answer helped!