When people argue about something, it is because they disagree. If they already agreed, they probably wouldnt be offering arguments for or against anything. Unfortunately, when people are in the midst of a disagreement, it isnt always clear to them or to others just what they are disagreeing about. Figuring out where the actual disagreement lies and where potential agreement might exist can be very helpful.
There are two basic ways in which people might agree or disagree: the first is in their beliefs (about what is true or false) and the second is in their attitudes. Disagreement about beliefs is the sort most commonly focused upon. People disagree about whether a certain type of diet leads to weight loss or weight gain, they disagree about whether a particular medical treatment actually helps people or is just pseudoscience, and they disagree about whether drugs should be legalized. All of these disagreements involve people adopting different and mutually incompatible beliefs.
The second type of disagreement, involving attitude, can be just as important as the first. Two people may agree that something is the case, but disagree completely on whether that is good or bad. For example, two people may agree that higher taxes lead to a reduction of some behavior, but while one may approve of this the other may find it to be intolerable.
If two people are trying to resolve a disagreement, they first need to understand exactly what they are really disagreeing about. If people disagree about beliefs, that is something which might be resolved by appealing to facts. When people believe that something is or is not the case, their best course of action is to try to determine what really is the case.
If two people disagree about attitude, however, appealing to facts wont solve anything. After all, people here arent disagreeing about something which can be proven right or wrong, but rather how particular facts should be valued. In cases such as this, we necessarily turn to more emotional language. While arguing about facts typically requires that we try to stay away from such emotional language, arguing about attitude will require that we focus on it.
Sometimes an interest in winning an argument can prevent people from seeing that their similarities may be stronger than their differences. Whether disagreeing about facts or attitudes, it can be very helpful in the long run to try to focus on areas of agreement first foremost. Areas of agreement may provide a foundation to build on so that those who are arguing can work towards a goal they share in common rather than the common goal of winning at the expense of the other.
Establishing areas of agreement can also help people find out if their disagreements are deeper than they suspected. Sometimes people will spend a lot of time arguing over what appear to be the real issues when, ultimately, disagreement on those issues can be traced back to disagreement over much more fundamental premises. Disagreement over whether God exists, for example, might be traced back to a more fundamental disagreement over whether authority and faith can provide knowledge that is as or more certain than reason and science.
Finally, looking out for areas of agreement can also help determine whether there is a genuine disagreement in the first place. Sometimes people think that they disagree about something when they dont. Common causes of this include misunderstanding how someone is using key terms, misuse of key terms, and even natural ambiguity in language itself. Sadly, it is all too common for people to become engrossed in a long debate which never would have occurred had they realized early on that they were using basic terms in completely different ways. Had that been made clear at the beginning, both the debate and the ensuing hard feelings could have been prevented.
This is why it is often so important to stop and define basic premises and terminology before entering into an argument: you cant very easily argue about whether God exists, for example, unless everyone involved as a clear understanding as to what they mean by God in the first place. You also cant have a productive argument about whether, say, pornography should be legal or not unless everyone involved is defining pornography in the same manner.
In summary, arguments involve or at least are supposed to involve people who disagree about some matter and who are seeking to arrive at some form of agreement. If that is the case, then reaching that goal requires a clear understanding about where the disagreements lie and what sorts of disagreements there really are. Understanding those matters will allow the argument to be productive and useful rather than simply a contest over who argues best.