If you want the apply button on the node detail page then you can make use of ctools link to get this functionality done.
All you have to do is implement a ctools menu item and a callback that will do the processing to send the users resume to the author of the node(job).
Then in the template file for the node you can add a ctools link by using the ctools_ajax_text_button() function of the ctools module.
For more details on how to imeplement this functionality. Please download and enable the ctools module. It has got a very good example module that will give you a clear idea on how to implement a the functionality you are looking for..