Finite difference methods (straightforward to apply, usually for regular grid) and finite volumes and finite element methods (usually for irregular meshes)
Each type of methods above yields the same solution if the grid is fine enough. However, some methods are more suitable to some cases than others
Finite difference methods for spatial derivatives with different order of accuracies can be derived using Taylor expansions, such as 2nd order upwind scheme, central differences schemes, etc.
Higher order numerical methods usually predict higher order of accuracy for CFD, but more likely unstable due to less numerical dissipation
Temporal derivatives can be integrated either by the explicit method (Euler, Runge-Kutta, etc.) or implicit method (e.g. Beam-Warming method)