Without a doubt, Death Knights are one of the hardest classes to face in PvP. Depending on the spec, they have multiple ways to handle various threats and seemingly have an answer to everything. While they are very powerful when played properly, they are far from invincible. Knowing how to avoid certain pitfalls will have you on your way to handling DKs more often.
First and foremost you need to know that a DK does not need you close to do damage to you. Depending on your class, they are just as comfortable kiting you as they are fighting you straight up. It should be reliably easy to tell what the DK wants to do compared to what you intend to do to him.
As a caster or a healer, he will want you up close and personal. In most cases these are the squishier classes, and as such he wants to keep you into melee range as much as possible. If you fall into one of these areas your best bet on survival is to keep your distance.
He is going to do everything possible to keep you from running. Your goal is going to be to increase your distance. Fears, roots, blink, are critical at this point as they will help you get away. Your crowd control at this point will likely force him to use his trinket, which is perfect as it opens you up to control the fight a little better. Unfortunately it will cause him to death grip you right back into melee range. From this point you need to escape again, and once you do you should have a slight advantage.
Melee classes need to get up close and personal to handle a DK, and as such the DK will usually opt to kite them. In these cases it is important to have any snares you have up. These include hamstring, crippling poison, frost shock, etc. These will allow you to keep him up close and personal. I will almost guarantee that he will be snaring you with his Chains of Ice making yours that much more important.
You should try to direct your attacks to the back of the DK to help you do more damage. Most mitigation is countered this way allowing you to do more damage.
It is worth knowing that a DK is not against standing toe to toe with another melee class. They wear plate which gives them a solid base of damage mitigation, so they do not needarily have to kite you. But you need to be ready to counter the kite if you blow any offensive cool downs to burst him down as that will likely be his primary defense.
Death Knights are not as difficult to fight as they once used to be. Simply having an idea on what they intend to do to you will give you an edge in the fight. There are many more things you need to watch for, depending on your class, but this should give you a solid baseline to work with.