Public displays of affection are out of the question. If colleagues are put in awkward situations, they won't thank you for it. Nor will management be impressed by your levels of concentration and dedication to the job.
Go into the affair with your eyes open. If your employer has policy on workplace romance, find out what it is and plan accordingly.
Never date the boss or someone who answers to you. The potential for messy situations increases the wider the hierarchy gap.
Don't let office gossip get to you. Once the affair is old news, tongues will cease to wag.
Try to keep a division between work and play.
When the relationship gets serious, explain the situation to your boss. Chances are, he or she already knows what's going on anyway. Good management values openness and professionalism and you'll get more from a discussion that doesn't catch you off guard.
Whether the relationship is going well or not, keep your cool. Work relationships, platonic or otherwise, are based on respect and your work reputation should never be compromised by what you do in your spare time.