After firing the shot, never take your eyes off the deer until you are sure it is dead.
If it has run off, carefully mark both where it was standing when you took the shot and where it disappeared from view. Watch, and listen.
You may hear the animal crashing off through the bushes and you may hear it fall, but whatever happens, stay where you are for an appreciable time.
Original advice was to sit tight while you smoked a cigarette but that is no longer politically correct and the advice now is, if I remember right, to wait 15 minutes.
(They must have smoked bloody enormous cigarettes!) Whatever, there is a very good reason for it all.
You do not need to reload your rifle instantly.
All that nonsense about a quick second shot is nothing more than neurotic crap because, generally, firing a quick second shot simply creates two cock-ups in place of the one you started with.
Take your time.
If the ‘dead’ animal tries to get up, then by all means take another careful shot; but please do not be tempted to try a quick shot at an escaping animal.
If the animal runs off and disappears, give it time to lie down and die.
If it is not dead it will at least have stiffened up and therefore be much less likely to run at your approach than would have been the case when it was hot and full of adrenalin.
There are all sorts of other things to think about if your deer has run off, but that would take an article and ought, perhaps, to be left to the more delicate and more professional touch of SG’s deer guru, Jon Snowdon.