How is a nondeterminisitic automaton running on an input? A nondeterministic automaton, after reading an input symbol at some state, may jump into any of a (finite?) number of states. 

Does the automaton uniformly randomly choose one out of the several states? 

So different runs on the same input will give different sequence of states? 

Does the automaton have to run in all the possible sequences of states on a given input? Or just one random run?
A non-deterministic automaton runs in all possible sequence of states on a given input. It is not a random run.

An input symbol is accepted only if in at least one of the runs it has reached an accepting state after reading the given input.

Hope this helps :D