Simple algorithm question - how to reorder a sequence economically

[Peter Brooks]

What is the easiest way to reorder a sequence pseudo-randomly?

That is, for a sequence 1,2,3,4 to produce an arbitrary ordering (eg
2,1,4,3) that is different each time.

I'm writing a simulation and would like to visit all the nodes in a
different order at each iteration of the simulation to remove the risk
of a fixed order introducing spurious evidence of correlation.