The first thing about winning an argument is to be sure you're right, or at least most probably right. The second thing is to make sure that you two don't actually agree on the basic issue, but disagree on details. (This happens more often than people think.) The third thing is to line up evidence for what you assert, and to state it after you state your basic premise. The problem is, of course, that your argumentative friend is going to challenge the veracity of your evidence, so what I usually do is to provide logical, deductive evidence first, rather than inductive evidence. It is more difficult to challenge evidence that proceeds logically from one step to another, whereas with inductive evidence, which is merely factual, anyone can say, "That's just not true." And then it just becomes someone's sources against someone else's sources. You have to agree to trust certain basal knowledge sources, in my view. Some of these might be: Grey's Anatomy, Keesing's World News Archive, Encyclopedia Britannica and peer-reviewed research from top journals. 
Certain topics are unwinnable, because they touch on immutable notions one has about so-called first things. Examples of these include gay marriage, capital punishment, and abortion. 
The internet and purposefully slanted news have created a world in which people complain about things that aren't true, or don't exist. They'll argue about how Obama is doing nothing about their high taxes when in fact he lowered them for most taxpayers (look it up - he did!) A top student of mine was convinced of the veracity of the so-called Philadelphia Experiment, in which it was suggested that the US Navy sent sailors time traveling during WWII. It is very difficult, but not impossible, to argue with such people. You have to begin by suggesting how far-fetched something like that is. It is the same with the "faked" moon landings, etc. You have to begin with unarguable facts, and proceed to the point of dispute. Then, ask your argumentative friend to confine his argument to just that point, just those facts: very frequently, he or she will be unable to do so. Then, carefully lay out why you feel that the facts lead most propitiously to your own hypothesis, and then restate it.