Death knights at their inception, were actually a pretty DoT and debuff-heavy class. As an unholy death knight in the Wrath era, I'd have Blood Plague, Frost Fever, Ebon Plaguebringer, and Unholy Blight (which was a separate disease back in those days) up as much as possible to get the full effect of both my DoTs and my weapon strikes. That's changed a bit over the years. As of Mists, Ebon Plaguebringer and Unholy Blight have come and gone, at least in the forms they once took. Still, keeping your diseases up is an important part of the death knight damage rotation, no matter how much we try to get around it.
With warlocks and shadow priests, this becomes even more true. Depending on their specs, Warlocks pretty much have to keep at least 2 DoTs up at all times, or their DPS drops through the floor. Shadow priests have similar dotting and debuff requirements. Learning to keep DoTs up on a class that depends on them makes it even easier to do it on a my death knight.
In addition, it was researching the warlock class that really got me into the idea of using a good DoT timer addon to keep track of my DoT uptime back in the day. That type of thing has become invaluable for making sure I keep my diseases up and only refresh them when the time is right.
Blow those cooldowns
Death Knights aren't necessarily known for massive amounts of burst damage. Retribution paladins and mages are a little better known for that. Luckily, I have alts of both classes. Arcane Power is probably the signature burst ability, one that struck terror into the hearts of PvPers everywhere back in the old vanilla BG honor grind days, and retribution paladins are the type that pray for a few lucky procs, then line up Avenging Wrath and Inquisition and go to town.
Death knight burst damage isn't quite as iconic a concept, but we can still pile on the self-buffs when the situation calls for it, especially frost death knights. Pillar of Frost plus Horn of Winter makes for a much stronger Raise Dead spell, for example, especially if you're high on a Time Warp at the same time. Playing a mage and paladin, where I was well aware of that burst damage because it was such an iconic part of the spec, has allowed me to become much more self-aware of when my death knight can pour on the damage as well.
The fine art of staying out of the fire
I tend to gravitate toward ranged DPS alts, overall. In addition to the mage and warlock above, my first alt was my hunter. She was also essentially my main for much of Burning Crusade. As a result, one of the most interesting and refreshing things for me is seeing how an encounter changes if you're ranged or melee. I don't necessarily mean it in the sense of "oh, ranged DPS have it so much easier," but that it gives you a different perspective on things. In some ways, you can get a sense of this by watching strategy videos, but nothing quite helps me out better than playing an encounter as a ranged class.
Being able to sit back and watch the encounter play out on a wider tableau can provide some pretty solid tips for me on what to do once I go back to my death knight. Let's face, it's generally easier, on most encounters, for ranged DPS to see, anticipate, and avoid "the fire," those magical spell effects that do massive damage and wipe the raid if they're not avoided or otherwise mitigated. When I'm on a ranged alt, it's a little easier for me to watch for these attacks and begin to see a pattern as to how they're formed, when they appear, and how soon I have to react to avoid them. Then, when I play my death knight, I find that I can remember what I saw on my ranged alt and move to avoid things, or at least pop Anti-Magic Shell at the optimal moment.
Get thee behind the mob
My first character and my main up until Wrath was a druid. I did a little bit of everything, including cat druid DPS. That means that for much of my career, Shred was the cornerstone of my DPS rotation, and to Shred, I needed to be behind the mob.
A death knight DPS has no such directional issues. You can wade in and hit the mob from every angle. The problem is, hitting the mob from the front has a lot of issues. You can get caught up in frontal cone or cleave attacks. Your attacks may get parried. Overall, unless the mob has a very specific gimmick that means you need to attack it from the front, you should be DPSing from the back or sides. Having played cat druid DPS for a long time, I find that I'm very aware of where I am in relation to what I'm DPSing, and I find it easier to pay attention and shift my position to stay behind the mob. It's too easy to get lazy or stop paying attention and drift to the front, but my experience as a cat druid has drilled into me that I need to stay behind the mob if I don't want my DPS to fall through the floor.
Of course, there's lots of small stuff too. You learn to appreciate what you have, like wishing I had Death and Decay while tanking on my druid. You get jealous of what other classes have, like wishing I had a Wild Imps style ghoul summoning passive on my death knight. The benefits to having a stable of alts are pretty comprehensive. That said, not everyone has the time, energy, or desire to cultivate such a stable, and that's perfectly fine too. But if you do have a chance to walk a few miles in another class' shoes, even if it's just watching a video or two or peeking over a friends' shoulder, you might be surprised at how much you learn.
Learn the ropes of endgame play with WoW Insider's DK 101 guide. Make yourself invaluable to your raid group with Mind Freeze and other interrupts, gear up with pre-heroic DPS gear or pre-heroic tank gear, and plot your path to tier 11/valor point DPS gear.