Submitting data through POST or GET is just a different way of performing an HTTP request. More specifically, in GET requests the variables are part of the requested URI, and in POST requests they're sent in a separate HTTP header. So Flash sends POST data in the same way your browser does; by adding a separate HTTP POST header.
The way in which it sends POST data kinda depends on what you're using. If you're using the LoadVars object, then it's pretty simple really: any variable/value pair that you set in the LoadVars object will be sent as POST data. So for example:
var lv:LoadVars = new LoadVars();
lv.myVariable = "myValue";
lv.send("http://www.yoursite.com/script.php", "_blank", "POST");
You will find that the myVariable/myValue pair is registered in the $_POST array.
Also, keep in mind that (last time I checked) the Flash IDE cannot and will not send POST data. You will need to test your SWF from inside a browser window to properly test POST capabilities.