As an employee, how should you handle a situation where you disagree with the direction given to you by your manager?
The only time to disagree with your manager is before the decision has been made. Even then it is providing a professional opinion not a disagreement. If you don't like the decision after it has been made, that's tough but it is your obligation as an employee to try to the best of your ability to implement it nonetheless. There are many factors besides technical that go into management decisions and you are not privy to all of them. The manager is paid to make the decision and is the one responsible for the ultimate outcome. There are very few occasions when a manager makes a decision that makes 100% of all subordinates happy.
Also do not ever disagree publicly with your manager after a decision has been made especially if there are clients or other outsiders present.
I think good managers understand that feedback, even critical feedback is appreciated when it is respectful and backed up by a good well thought out reasoning. Everyone regardless of level should appreciate the point of view of others.
However; It's important to understand who the people making the decisions are and when a decision is final. Pointing out a well thought out idea, or pointing out a solution to a problem that might be different then your boss's is great, hammering your boss about the same thing just because you think he is wrong is not. I use the 1.5x rule myself. Bring up the solution once during discussion, if your boss decides not to follow that's fine, let it go. Only bring it up again if a specific case could be solved using your solution (The .5). "I think this might be a good case for that archiving solution we talked about last month". Anything more when your boss is not receptive can be seen as offensive.
This is based of my experience in US customs, different cultures will have radically different beliefs.