Wikipedia seems to cover this well, with quite a neat example!
Sorry, I am not entirely sure what you mean by movements then. An automata consists of a 5-tuple, where is the set of states, is your alphabet, is your transition function (lines), is your start state and is the set of terminating sets.
Which of these are you wanting to be empty, if any?
This should be in your lecture notes:
Let be a non-deterministic automaton with epsilon-travels ("empty movements")
Then the equivalent non-deterministic automaton without epsilon travels is where:
(this means that any state that was reachable from with epsilon-travels and input , is now reachable from only with input )
and
if then
if , then
Sure:
Take a look at the images I attached. The one with EM is the original automaton, and the one with ND is what it should look like after the 'conversion'.
http://img821.imageshack.us/i/28510076.jpg/
http://img202.imageshack.us/i/51132577.jpg/