[writing a plugin] wordpress undefined function

hello, I’m making a plugin for wordpress, It always happens the same problem with the wordpress plugins that when I load with ajax echo text from a php page (called directly) gives me error on wordpress functions, they are undefined: when the call is directly the php page is seems to be outside wordpress

even if I do include the main file of the plugin gives me errors eg. on get_option (‘siteurl’), has happened to someone? how can I solve it?

I have to do this: filling out a registration form if user is already registered when he enter his email and password the form is all filled with ajax, ajax is working but I can not get the other fields in the db because it gives me error on

Call to a member function get_results () on a non-object

although if there is

global $ wpdb;

coul you help me??than you