I'd say a week or two as well, and how you approach it depends on whether you've sent the resume to HR or directly to the hiring manager. In my organization, all resumes must be submitted to HR first; they screen and pass along the ones that look promising. If you've sent the resume directly to HR, you can call to verify that they've recieved, but you probably aren't going to get much more information than that, and most HR departments are so overworked these days that you may not even get an acknowledgement that your resume has been received. If you've sent directly to hiring manager, then follow up a week or so after they've received the resume. You may or may not have any luck with introducing yourself and asking some questions about the job/organization, depending on how busy the manager is at that point. Best approach would be to say "I'd love to ask you some questions about Company X and your department, when is a convenient time for you?"