First of all we need to understand that a snake will never approach humans. If you are sitting or lying absolutely still for a long time, the snake might not consider you a danger and therefore risk to trespass close by, but even this is unlikely.
So, most likely, it is the other way around that you approach the snake. In this case we need to differenciate between venomous snakes and constrictor snakes (eg. python).
Constrictor Snakes
Even the biggest python is extremely unlikely to see you as food, so just walk passed with a little distance and you will be fine.
Venomous snakes
Venomous snakes dislike the presence of humans and will leave as long as they have a chance. Usually you won't even realize the snake because it will have already disappeared before you arrive. Snakes have a very sensitive sense for vibrations in the ground and can tell your steps from far. Hence, they will be gone before you get there.
If you happen to catch the snake unaware, just stop where you are and make sure you leave the snake room to escape. Of course it depends on how far away you are from the snake, but if you are out of reach for the snake, you can simply walk away. If you happen to be very close, just don't do any abrupt movement. The snake could mistake a sudden movement for an attack and will defend itself. If you move back slowly, you will be fine. Don't worry, the snake won't follow you, it has absolutely no reason to do so.
There are however 2 exceptions:
The spitting cobra
The spitting cobra can spit venom into your eyes from up to 2 meters distance with remarkable accuracy. This happens so fast, you will hardly see anything happening. If untreated, the venom can make you loose your eye-sight.
The puffadder
The puffadder relies on it's camouflage and will not escape. When it senses your approach, it will freeze and hope you don't see it. Again, this snake will not bite you unless it feels threatened, but this is more likely to happen because you havn't even realized it is there. Most snake bites reported are actually from the puffadder because of this reason and this makes the puffadder the most dangerous snake in Africa. People very often step on it or reach for something that is right next to it in which case the snake will - of course - bite.
But like all other snakes, as long they don't feel threatened, they won't bite. I was sitting with a whole group of friends on a staircase to a jetty and we were just chatting away for at least half an hour when one of my friends pointed out in a very strange way that he will now slowly get up and look for a better place to sit because he just realized that he had been sitting 20 cm away from a 1,5 meter puffadder!! He had mistaken it for a rock. He carefully got up and that was it. The snake didn't move a millimeter. It didn't feel threatened and hence it remained where it was.
You can imagine what would have happened if he would have jumped up suddenly or touched it accidentally before realizing it's presence.
In general it is wise to walk on footpaths where you can see what you are stepping on. I know, especially when on a bush-walk, there are plenty of fantastic things to see, but please keep an eye on where you place your foot as you walk along.
In a Camp / Lodge: Should I report a snake to staff or management?
In most cases the staff will do everything to kill the snake. Many Africans have a strange urge to kill any snake they come across. Personally I suggest you get your camera rather than a member of staff. If you feel very threatened by the presence of the snake, do speak to the management but kindly ask them not to kill the snake and watch them remove it. First of all you will get to see this beautiful creature even more and secondly you can be sure they don't kill it.
Oh, and one last thing: The only snake which is so poisonous that it's bite will kill you instantly, is the Hollywood-snake. It has been seen on TV many times, but never in reality. With all other snakes you have plenty of time to get an antivenom.