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You use Apache's .htaccess/mod_rewrite, and optionally a PHP file, which is the approach I like to take myself.
For the .htaccess, something like this:
RewriteEngine On
RewriteRule ^(.*)$ index.php
Then in your PHP file, you can do something like this:
The following should get everything after the first slash.
$url = $_SERVER['REQUEST_URI'];
You can then use explode to turn it into an array.
$split = explode('/', $url);
Now you can use the array to determine what to load:
if ($split[1] == 'home')
{
// display homepage
}
The array is starting from 1 since 0 will usually be empty.