A bitten human (or any human that has had zombie tissue or bodily fluids introduced into their body) will certainly reanimate into a zombie.
A bitten survivor is discovered
Speed of the transitition depends on the overall health of the host, proximity to a major blood vessel, and type of zombie attacker. Killing the human before he transforms is almost always the safest option, but it is rarely easy, as humans tend to bring their loved ones along or develop strong emotional bonds in the process of depending on one another. The emotional attachment may cause irrational actions, such as refusing to acknowledge the inevitable change. Disputes over killing infected humans are one of the leading causes of survivor group failures.
One method that might buy some time and safety while the decision is being made is to strongly tape shut the jaw of the living survivor or handcuffing him to a heavy object. This will render the eventual zombie unable to bite if the transformation occurs ahead of schedule. Immediate amputation can also be performed, but this has a small chance of success and may be lethal anyway.
The unknown addition to one's survivor group should always be suspected as a potential infected host until proven otherwise. A strict strip search policy is advisable, but not always practical or enforceable. Another alternative is a holding cell, where the potential additions stay past the incubation period of the illness.
Notes: From a more realistic stand point, a virus would be able to be killed with bleach, fire, or any known anti-viral purification method, thus making amputation unnecessary, though it would need to be done quickly; it would be best to test this method on a survivor who has been freshly bitten on an area that can't be amputated, like the neck or chest.
Also, in some cases such as the Walking Dead, simply death with the brain intact will cause reanimation. In this case, it means that being bitten will not be the cause of reanimation, people die from open wounds and diseases from the zombie. Therefore immediate patching and sterilization of the wound will save those who are bitten.