All the API methods work on a web pull basis so you simply need to have the ability to get the response to the listed method url. Then you simply need to break down the return and display as you see fit.
For example in PHP:

$return = file_get_contents(method_url+required PARAMETERs);
Echo $return;

The above will print out the raw return from any given valid method url

Getidents will return a list of all the leagues we support in the format shown here Link: www.footytube.com/openfooty/service.php?package=Le...

The results are paged at 50 per page so you will need to move through the pages to get all the ID's.

To do so simply use the GET variable &page=1 and increase the page number. In the element leagues there are the attributes hasMorePages and nextPage these will tell you if there are more pages and what the next page number is