There are two main techniques.
the first is to arrange a sequence of still cameras along a fixed track which is equivalent to a camera move. To completely freeze the shot these will all take an image simultaneously, for slow motion they can be fires in a sequence equivalent to the frame rate you want to achieve.
It is also possible to combine this with either a motion control video camera on the same track either simultaneously or in two separate shots which are later composited together.
Alternatively you can use a high frame-rate video camera with a fast motion control to achieve a similar effect with a single camera.
In some cases you will have an actor moving in real time with events around them eg a crowd or explosion happening in slow time or vice versa. This can either be done in green screen or by compositing different motion control shots together. In some cases you can get a wide range of frame rate by having one set of actors perform in actual slow time or keep as still as possible.
Its also not uncommon to use depth of field and possibly forced perspective camera effects to further enhance the sense of unreality.
As is often the case in film it is often a a matter of combining physical, camera, digital and post production effects to get exactly the result you want.