From PHB3, p217, Full Discipline (emphasis mine):
Separate Actions: Each of the techniques in a full discipline power requires a separate action to use. The action types are specified in the power. You can use the techniques in whatever order you like during a round, and you can use one of the techniques and not the other during a particular round.
So you can use just the move, or just the attack, or both the move and the attack.
Note that you can still only use the move power once, unless it's an at-will power (like
Crane's Wings); from the same section:
The number of times you can use a technique during a round is determined by the power's type - at-will or encounter - and by the actions you have available in that round. For example, you can use the techniques of an at-will full discipline power as many times during a round as you like, provided you have enough of the required actions. If you use an encounter full discipline power, you can use both techniques, but can use each technique only once during that round.
Thus a monk could use the move action of an at-will Full Discipline power (such as
Crane's Wings) twice in the same round, but could not use the move action of an encounter Full Discipline power (such as
Drunken Monkey) twice in the same round, nor could they use the attack power twice in the same round even if they had sufficient actions to do so (from spending an action point or otherwise).