When you use your company's employment terminal, you'll find new options for both employees and management.
REQUEST REIMBURSEMENT
This will collect a description of your reimbursement reason, the amount being requested as well as a brief 'budget code' for your part of the company (ask your boss). example budget codes: VS-RND, NLM-TV.
YOUR REIMBURSEMENTS
View your requests pending review, those that have been approved and those that have been resolved (paid or denied).
REIMBURSEMENTS
If you have the management rights on the employment terminal, you'll be able to approve and deny reimbursement requests via this option in the MANAGE EMPLOYEES sub-menu.
Approved reimbursements should pay out when you're able to collect your weekly pay. Note I say should as I have yet to test the change to payout, so please report bugs if you encounter them. :)