I've kicked this idea around a few times. It's partiall inspired by one of the other MMORPG.com bloggers (specifically Paragus1's http://www.mmorpg.com/blogs/Paragus1/122010/21294_PvP-For-Dummies), but while the other post mainly is aimed at world pvp (and does quite a good job at showing newbies how pvp works in an MMO), my aim is to give very broad, general tips that can be applied to MMOs of many genres, and maybe most gaming against another player. These aren't all nub tips, since we've all met the "Day 1" vet who your girlfriend/little sibling/nub guild mate can easily kill, simply because this person hasn't done some critical thinking.
1. Learn to play the game.
Now, hold a minute, I don't mean "l2play" as trolls usually note it. I'm specifically referring to understanding the game in both theoretical terms and actual performance. Learning to play doesn't in and of itself make one a better player, but a wiser one. When people don't know what their enemy can do, what their own moves can do, what the developers want from players, the goals of an instanced PvP encounter, etc, critical errors generally arise.
Let's go with something concrete. If you play a class where a certain amount of moves only work on NPCs, and other classes do not have said restrictions on their moves, then you are playing a pve class. Complaining that you have trouble in pvp may be valid in some aspects, but the fact of the matter is that you have a decent warning that you are trying to put the round peg in the square hole. Learning how the game's aims and your play work (or don't) it critical in early skill development.
Look at the game's goals and ideals. See how people's play goes with or against those ideals. Look at what works and what doesn't. If you're always losing in battles, ask yourself what you did wrong. Pointing the finger is easy, but it's much harder to change other people than it is to change yourself. I constantly have people in theme-park MMOs complain about how bad our side does, and end up grouping with them. 9 times out of 10, the person complaining is also part of the problem, and on my own, I can make the game go much smoother (unless someone's watching a good movie nearby; then we're doomed). I don't say this to brag, but to mention how much of a difference a single player who knows what they're doing can make in a situation where many players simply don't understand how to play their characters, what moves the enemy has available to them, and how to achieve victory objectives (whether a player or a developer defines them). My general tip: if you constantly see an issue, ask what you can do to fix it. Not how you can explain it to others, but how you can get it done.
While one can often find interesting combos that allow, say, a healing class to 2 shot people, this sort of thing is usually something you should know will get nerfed. Game design philosophy and practice are supposed to line up, and more often than not, developers will do what they can to make sure this happens. You are free to play the way you want, and I personally encourage testing the game's limit (but don't break the system, just make sure you understand the boundaries so you know how it works).
2. Show, don't tell!
Your writing teacher told you to do this all the time, and the same applies to gaming. This may sound like it'll conflict with #3, but let me put it to you this way: when people see you do something effective, ranging from getting an instanced pvp objective completed to locking down an enemy, it makes a huge impact. People may ask, on the spot, how you did it. I know that to me, personally, getting PMs or public statements that I did something amazing (or having the enemy shout out my name as a target to watch) is how I know if I'm a good player or not. Theory crafters are everywhere, but it's difficult to argue with results.
I know, it's sort of against #2, but here's the thing. Anyone can say whatever they want, IRL and in video games. Unless you can point to the smoking gun, talking may not do a lot. You can't always do this, but when possible, on the spot, as you do it (or as soon after), let your friends/team mates/guildies know exactly what you did to get your results... ok, maybe not saying something like "I hit 3, 4, tab targeted twice, hit shift 1..." but what decisions you made and why. I've gotten stuck with some bad players in the past, but explaining to them why you make certain decisions helps a lot in the long run. More often than not, you'll hear "I dunno," "I'll do it my way," "Leave me alone," etc, but when you see the results, and get that rare player that says "I tried it your way... and you were right," it helps make sure that there's 1 less nub playing your game (and hopefully willing to pvp with you in the future!). For every player you convert, there is potential that they too may convert others. Elitist guilds are nice in that you may not have to train anyone at the moment, but unless you run real tight, at one point or another (and with most elitists I've grouped with, fairly often) you'll end up having to play with random baddies. Do yourself a small favor and try to build up your gaming community so that the local baddies you play with are hopefully a bit better than your enemies'.
4. Learn to beat yourself.
This is similar to #1, but slightly different. With all the information at their finger tips, few people realize that at the end of the day, you need to see how it's going to be used against you. You're not the only one out there with most of this information, and modern day MMOs tend to have communities that share information at least throughout their guild. If you know what others perceive as your weaknesses, and know how they will attempt to counter it, all that's left is coming up with your personal counter.
Let's go with a real example from WoW's arenas. Most people look at a team that has 1 healer and 2 DPS and think "Ok, kill the healer first." Most teams will do that. However, another team with the same composition will probably also know this general strategy. Instead, what they'll try to do is kill off the DPS first and prevent the healer from doing their job, either by CCing the healer or by putting DPS in positions where they line of sight away from their healer. Without the DPSers around, most healers won't last too long (naturally, this is not always the case, but the counter is less known to players who don't consider their own team's weakness).
5. Look at risk vs. reward.
Most people talk about this in terms of general play mechanics: "why should I world pvp, where I can get camped, have to run to my body, and make little pvp currency, when I can solve all of those issues by running an instanced pvp mission." Yes, super, you're killing the game creativity (but that's a rant for another day ;P).
No, what I mean is, ask yourself what can go wrong and how bad it is. In Darkfall, death means losing everything on your body 9 times out of 10. Ask what victory means, and then decide what you're putting on the line for it. If, for example, you are going out fully geared to gank newbies, you have very little to gain and a whole lot to lose, so it's probably better to keep your best stuff at home.
On the other hand, if you're playing in World of Warcraft, death usually means nothing (outside of arenas, and only if you care about rank). The worst thing you can do is be afraid to die. No, constantly dying isn't usually a great strategy, but it's more useful than in Darkfall's world pvp. While death in DF can really set you back, death can be used in WoW to, for example, distract the enemy team into thinking they need to defend a node with multiple people, allowing your team to fight 1 less person in assaults on other nodes. Dying may suck, but your team is only losing 1 person while the other team loses every person waiting at that node who wants to kill you. No, it won't put you on top of the damage meters, but damage meters don't win games, strategies do.