Person A advocates position p.
Person B asserts that A's past actions or statements have been inconsistent with position p
Therefore position p is false or (when used as a red herring) p is abandoned.
Dad: "John, you shouldn't smoke. It is very bad for your health!"
John: "You smoke, so it must not be that bad for you."
The obvious error here is that just because someone is acting hypocritically doesn't necessarily mean that their argument is wrong. In this particular example, the hypocrisy could actually serve to strengthen the fathers argument since he has personal experience dealing with addiction and the damaging effects of smoking.
Teacher: One should always recycle paper, plastic and glass products. I'ts good for the earth and it's good for future generations.
Student: Ha! I saw you throw your soda bottle in the trash after lunch! Why should we listen to someone who doesn't practice what she preaches?2
Again, it is important to realize that the merits or truthfulness of an argument are not typically tied to whether the source of the argument consistently follows his or her own position. It could very well be the case that both recycling is good for the environment and that the teacher does not regularly follow her own advice.
This is not to say that pointing out hypocrisy is always wrong. There are times when a persons credibility, character or perhaps even their right to make an accusation are the issue.
Mary: I'm just appalled at my sister-in law. She had an affair and then when my brother found out, she expected him to forgive her. That sort of thing is unforgivable, I think he should leave her. It would be good riddance to bad rubbish
Francine: Cool it Mary. I know about the little extra-marital fling you had a couple of years ago and when your husband found out, you were grateful when he forgave you.1
In this example Mary's right to be appalled is the issue and as such it is appropriate that Francine point out her hypocrisy.
1. Critical Thinking: An Introduction to the Basic Skills - 5th Edition. William Hughes & Jonathan Lavery
2. Informal Logical Fallacies: A Brief Guide. By Van Jacob E. Vleet
RationalWiki - Tu quoque
The Nizkor Project - Tu Quoque