Don't broadcast that you're dating someone. Send any cards, gifts or flowers to the home, not the office. No physical contact in the office. No secret kissing, caressing, hand holding or sex in the office. People get caught and careers can get ruined.
Business rules apply in business-related social functions.
At the office party or any business social function do not drink too much, wear seductive clothing, do not dance too closely, and no seductive language. If the relationship fails-be professional and adult about it. Even if you've been jilted and the relationship ends badly you cannot vent your negative feelings in the office. This is the risk of office relationships. They sometimes don't work out and then you have to continue to see or work with the person everyday.