I. Rendered motion blur

In the render settings, turn on motion blur in the camera section of the Vray tab. Set it to:
• Duration: 2
• Interval Center: 0
• Shutter Efficiency: 0.5
• Geometry Samples: 8

See the Vray docs for detailed explanations of the above parameters. These settings use more blur than is physically accurate (duration 1), making it twice as blurry, but this looks nice. The geo samples are especially important with things like helicopter blades (the above settings means it samples the geo's location 8 times within a single frame) where you will likely need to sample the geo more.

Physical camera
Note that if using a physical camera, it will override the camera settings in the render settings, and motion blur needs to be enabled in the physical camera directly. Here the motion blur is controlled by the shutter speed (longer shutter speeds produce more blur). As the shutter speed is changed, the image brightness will also be affected (a longer shutter speed = brighter picture as more light gets in), so the f-number (the aperture) needs to be increased to compensate (The higher the f-stop, the smaller the aperture hole is, meaning it lets in less light).

Motion blur and dynamics simulations (geo caches)
Rendered motion blur works by comparing the location of a geo's vertices at different frames. For geometry caches of dynamic simulations, such as water splashes, each frame has a different geo, with a potentially different vertex count, making this comparison impossible. As a work around, a velocity map is mapped to the vertices of the geo for each frame, and exported with it as part of the Alembic cache. Maya's Alembic import cannot read this information, so Alembic caches of dynamic simulations must be read in as a Vray proxy, which automatically recognizes this info, and renders fine with motion blur.

Another method is to render a velocity render element and use that in comp to generate motion blur. This process is described here. The disadvantage of this approach is that it can only generate blur in one direction, and so cannot blur movement that is going in multiple directions at once, like a splash or explosion or even someone waving both arms.

This is the simplest method. You just add a motionBlur node (or the new motionBlur2 node) in Nuke. It looks at every pixel on each frame, tracking where it moves to on the next, generating blur based on this. It can therefore produce blur in multiple directions (unlike a velocity pass) and is super fast (unlike rendered motion blur). It does sometimes produce ugly artifacts which can require some roto work and other comp tricks to hide.