Just like in real life, if you want to apply for a job at one of the corporations that transparently control every aspect of your life, you're going to have to get your paperwork in order. Firstly, you'll need your @history to be approved, and secondly, you'll need a resume.
Your resume does not need to be as complicated or in-depth as a real life job application.
The only absolutely necessary details are your character's contact information: include your SIC name, as well as your phone number and gridmail address if you have them. You will also need to provide your credentials, listing any skills or accreditations your character has, as justified by your approved @history. Consider mentioning your character's talents, any college degrees or licenses your character has acquired, accolades you've received, previous positions you've held, and so on - anything you think would be relevant to the job you're applying for.
Your resume can be handwritten on a letter, but if you want to come across as more professional, you can send your resume electronically or have it printed out; find out in character what equipment you'll need access to in order to do this. You'll also need to find out who you need to contact within the company in order to hand off your resume. Try asking a receptionist at the corporate office, and a GM will be happy to help you get on track if one is available. If you're unable to get a response from someone in the company, tell the NPC your contact information and leave a @note about your interaction with them.