Even though theory debate should only be used when your opponent is actually being unfair or uneducational, that won't always be the case. Many people use theory as a strategic tool in order to layer the debate and overall increase their chances of winning. Even if their use of theory is justified, you want to have the tools to be prepared to beat back the argument and still win. With theory becoming a more prominent feature in Lincoln-Douglas debate, knowing how to adequately deal with it is more important than ever. In addition to understanding the structure of theory, there are a variety of tools you can use to efficiently deal with theory.
Counter-Interpretations
The first step in responding to theory is to establish a counter-interpretation. This competing interpretation is a rule that you believe is acceptable for debate that you do not violate. The key component of picking this rule is that it should be competitive with the original interpretation. What I mean by that is that it should be impossible for both rules to be enforced at the same time. If they could both be enforced, then your compliance with this rule does nothing to undermine your compliance with the other. However, if they are competitive and you show that your rule is better, it's irrelevant whether you satisfy the other rule or not.
In general because you only care about compliance with your rule and not whether someone is violating it, it's ok to have your rule be permissive rather than prohibitive like interpretations should be in general. Again, this mean you can (and should) state as your rule that you may define the death penalty as X. Doing so makes your position sound more reasonable and believable.
Dealing with the Violation
Responding to the violation is most applicable when you don't actually violate the rule set out by your opponent. If it is actually the case that you do not violate or it is possible that you don't, then you should absolutely make the "I meet" argument, which is basically that you meet all of the rules presented. This can often be enough to dismiss a theory debate as it doesn't matter how good the rule is supposed to be if nobody is breaking it.
Alternatively, you can argue that your opponent is also breaking that rule. In that case, you would not lose because your opponent won the theory debate because the reasons given as to why you should lose also serve as adequate reasons as to why they should lose. These arguments tend to be much rarer as it would require a fairly large blunder to make such a mistake, but mistakes like this do occasionally happen.
Standards
The way you respond to the standards is the exact same way that you respond to other arguments. You should be making both offensive and defensive responses to these arguments, as the only way they differ from normal contention arguments is that they deal with different issues.
When responding to theory, in addition to just beating back their standards, you can also offer competing standards by which to compare your arguments. It is worth noting that this strategy is only acceptable if you have a counter-interpretation. Without one, there is nothing to compare to, and so putting forth new standards will often not do much by the way of improving your chances of beating back the argument.
Voters
When responding to the voter section, there are generally two methods of doing so: answering the voter directly and using an RVI.
Answers to Voters
Responding to the voter directly while one of the least successful ways to deal with theory is worth mentioning. The principle is that if you can demonstrate that things like fairness or education should not be voters, then that's enough to dismiss the truly bad implications of theory. The problem with this rationale is that most everyone has come to accept that fairness and education are good things. Thus, taking this approach will be an uphill battle. However, there are advantages to such an approach, as these types of arguments are fairly basic and can be made in large quantities, overwhelming an opponent.
RVI
The RVI, or reverse voting issue, is one of the most controversial issues when it comes to responding to theory. Essentially, an RVI makes the argument that because theory is a no-risk issue for the person running it, they should be punished if they lose theory. When most people run theory, the person running it will never lose because of theory, only the person defending against it can lose. As a result, the RVI is an attempt to level the playing field.
A lot of the difficulties with running this argument are the inherent prejudices people have regarding the argument. Many people think that inherently the RVI is not a valid argument. The reason for this is that the claim boils down to an argument like, "I should win because I was fair". This claim in general has trouble, but there are many judges who accept the RVI, and if you respond well to its objections it can be rewarding.