The basic approach to this is something called Dead Reckoning and a quite nice article about it can be found here. Basically it is a predication algorithm for where entities positions will be guessed at for the times between server updates.
There are more advanced methodologies that build on this concept, but it is a good starting point.
Also a description of how this is handled in the source engine (Valve’s engine for the first Half Life game) can be found here, the principle is basically the same – until the server tells you otherwise use a prediction algorithm to move the entity along an expected path – but this article handles the effect this has on trying to shoot something in more depth.