Undoubtedly, Death Knights are one of the complex classes to challenge in PvP. Depending on the spec, they have multiple ways to handle numerous threats and apparently have an reply to everything. Whilst they are positively competent when played properly, they are far from beatable. If you know how to refrain or stay away from certain pitfalls will have you on your way to handling DKs more often.
The first thing you need to know that a Death Knight doesn't need you close to do damage to you. Depending on your class, they are just as content kiting you as they are fighting you straight up. It may be relatively straightforward to tell what the Dark Knight wants to achieve compared to what you are determined to do to him.
Since he is a healer or a caster, the Dark Knight will desire you up close and personal. In the majority of cases these are the squishier classes, and because of that he wants to keep you into melee range as much as possible. If you end up in one of these areas your best chance on survival is to maintain your separation.
He is going to do everything possible to prevent you from running away. Your aim is going to be to widen the distance between you and him. Fears, roots, blink are imperative at this time as they will help you get away. Your crowd control at this point will more than likely push him to utilize his trinket, which is perfect as it helps you to control the fight a little better. Regrettably it will compel him to death grip you immediately back into melee range. From this point on you will need to run away again, and once you accomplish that you ought to have a slight advantage.
Melee classes have to be close and personal to handle a DK, and because of this the Death Knightwill ordinarily opt to kite them. In these specific cases it is very to have any snares you have up. These include hamstring, crippling poison, frost shock, etc. These will allow you to keep him personal and up close. I can practically guarantee that he will be snaring you with his Chains of Ice making yours that much more vital.
You ought to try to focus your attacks to the back of the Dark Knight to help you do more damage. Most mitigation is countered in this way allowing you to bring about more injury.
It is worth noting that a DK will stand toe to toe with other melee classes. They wear plate which gives them a solid base of damage mitigation, so they don't necessarily have to kite you. But you need to be ready to counter the kite if you blow any offensive cooldowns to burst him down as that will more than likely be his first defense.
Death Knights are not as difficult to fight as they once were. Just having an idea on their intention will give you with an edge while in the fight. There are a number of things you will need to look for, depending on your class, but this will give you a solid baseline to work with.