The Man Overboard is a classic survival at sea scenario, you're working far out to sea on a vessel/installation and you witness a man falling overboard. With no time to prevent this what happens over the next few minutes will affect the outcome. Panicking and loosing it aren't options here. This is a time for cool heads and swift action.
As the Watcher/Observer...
Keep him in sight at all times and call for assistance 'Man Overboard! Man Overboard!' over and over again. While doing this follow his movements in the ocean and move to the nearest life lifebouy.
Hopefully while you're doing this either the nearby stand-by boat will of either spotted what's going on, or had the control room call out the emergency to them. Or if you're on a vessel at sea the crew will launch the Fast Rescue Craft (FRC). Ideally, almost straight away help should be on its way to the casualty. Keep the casualty in sight all the while. With you as the eyes on the casualty you've got a position and eye to direct the FRC crew into his position where hopefully they'll pick him up.
As the Falling Man...
They'll be no time for anything once you've fallen, you're going in the sea now whether you like it or not. Depending on the sea state you'll have to brave a real shock to the system. Not only will the cold water cause you to take a sharp breath inwards but depending on how agitated the sea is you'll quite possibly suffer on impact. The more agitated and therefore aerated a sea is the less harsh a landing you'll endure. This is paradoxical in the respect that a 'softer' landing will mean a rougher and wavy sea state (usually) you'll have to struggle with. However at the other end of the extreme is broken legs and arms if you land badly. The best landing position is arms across the body with hands on either shoulder in an 'X' and keep your elbows as tucked in as possible (you risk having both shoulders dislocated otherwise). Look up before you hit the water too. All this is probably difficult to do though because most people will panic and flail about mid-air.
Once in the water deploy your life-jacket (if worn) and make sure it doesn't put you in a 'face-down position'. Deploy a spray-hood if it's got one and start waving your arms to attract attention. If people are looking out for you they'll be looking for these signals and signs. Some say you ought to scream and shout but this will probably be pointless if you are at a distance with the wind and sea making sounds. If the weather is calm the best thing to do is to float on your back and wait for any life-buoys that are thrown to you otherwise assume the vertical. If the thrown buoy is on a spool tether and you catch onto it it'll prevent you drifting too far.
Falling overboard from an offshore installation is more dangerous in some respects than a vessel at sea. You may be unlucky enough to strike protrusions such as vent pipes and walkways or other metalwork resulting in bad injury's. As if this isn't bad enough the waves and waters that run through a platforms support structure can be turbulent indeed and you could be dashed against the sides and supportwork if you're carried inside by the current. This may work to your advantage if you can swim well. Running up and down certain support legs of an installation may be ladders (for evacuation purposes). You might be able to reach one of these and self-rescue. If this isn't possible try to relax and be calm. If you panic and lose your cool you'll form tunnel vision and lose perspective on what's going on around you.
The Fast Rescue Craft crew are well-trained and good at recovering casualties in the water. Don't fight or try and climb aboard under your own power, you'll likely be exhausted and might make their job harder than it is.