Designing An API with PHP/MySql

How can I design a system that let other people modify record from another
server? Like

I have registered member on my site, people can use external application to
check if the

(1) user is registered

(2) user is online

(3) update user profile on mysite



Like the myspace.com stuff, I saw I php class from phpclasses.org that you
can use to modify your profile from another server.

So I want to design something like myspace, but sometime I will want others
to be able to check if a user is registered or online on my system.



I want to use PHP/MySql.

Please I basic example/article link will be appreciated.