DK is my secondary in singles and my main in doubles.
Down B: Covers about a third of FD (IIRC). The range on this is huge compared to Melee. It interrupts most grounded approaches, and manages to even clip a lot of short hopped approaches on the way in. I use this liberally to control space in front of me (and behind!) and pop my opponent up in the air for mixups. My options are reverse backairs, neutral air, dash attack, and tilts, depending on where my opponent DIs.
Bair: You can throw this out twice on a short hop. The range is hot. The dmg is hot. The knockback is hot. Use this liberally.
Nair: Underrated in general. It comes out super fast and ends super fast. When I first picked up DK, i used this a TON until I got used to his spacing.
Fair: Kills in more ways than one. Hit with it early in the animation, and it will star KO off the side. Hit late, and it spikes HARD. This is my favorite flashy kill move with DK, but it is often airdodged. use it a few times to bait the airdodge later, then punish the airdodge with Dair or Nair.
Dair: Great spike. The spacing/timing is a ***** to get used to, but if you practice with it enough, you can get some really nice low% kills with it.
D-Smash: Your bread and butter kill move. It comes out way too fast for how heavy DK is. This move is the reason why DK is good. He doesn't have problems getting KOs because he can drop Down smashes on you FAST. Kills metaknight at retardedly low %s. (I don't memorize the numbers. Someone else can post them.)
Up Tilt: Pops grounded opponents up, just in reach for another Up tilt (if they are at low %s). You can often chain 3 up tilts in a row on some people, for a quick 15-20% (again, i don't have the numbers memorized). Up tilt reaches into the platforms on most stages, and sets up Up air.
Up Air: Another decent KO move if you can get it off. It's harder to land than even his Fair, unless your opponent sucks, or you can trick them into air dodging at the wrong time. Sometimes I'll jump up at them and nair instead of Up air, they'll airdodge if they predict the Up air, and you can punish with another Nair, or even an Up air sometimes.
F-Smash: Geez. This kills at such low %s. It's not all that slow either. If I'm playing defensively, I'll throw out Bairs while moving away from my opponent, and if they chase, I try to land and immediately C-stick towards them. They often fall into it. I don't save F-smash for kills, since D-smash does the job so well, but you can if you want. It's just a little slower and only hits on one side.
Donkey Freaking Punch: I'm probably rare in the DK playing community because I don't use DK Punch much at all. It's kind of gimmicky if you ask me. I don't spend all my time trying to abuse super armor, because I'd rather just not get hit. An interesting note on DK punch is that it is better with 9 charges than with 10. One thing that's fun with a charged one is to throw it as you are recovering from up high, and try to catch your opponent with it while you are in the air. Often times, the Super armor will keep you from getting edge guarded, and you might even hit your opponent with it too. Again, this is all kinda gimmicky and I usually just stick to bread and butter DK.
D-Tilt: I love down tilt. The range is awesome. It trips. It infinities on walls. When my opponent can't be killed by a D-smash, I use D-tilt to space, since I can usually connect with 2 before they DI away. If they trip, I often follow up with dash attack or a reverse bair.
Up Smash: Nice kill move with good range. I use up tilt instead if they are low, but after about 65%, I look for up smashes instead.
Up B: Use this on the ground like Bowser does. It's not as good as his on the stage, but still pretty good. Recovery-wise, it's actually pretty godly. On most characters, you'd be hitting the edge, but DK can actually fly over the edge and land on the OPPOSITE EDGE. It recovers SOO far. Unfortunately, ALL the energy DK spends traveling with Up B is SIDEWAYS. His vertical recovery sucks donkey doodads. All it takes to SD with DK is air dodging ANYWHERE near the ledge. By the time you recover from the air dodge, you are already too low to recover. Jamming B quickly helps you get more height, but not by much. You'll get stuck under flat edges like PS1 a LOT if you aren't careful. Spacing a sweetspot on Delfino, lylat, halberd, etc can suck sometimes. Expect to get forward smashed as you are recovering. Counterpick to stages that don't have janky ledges. If you are playing against DK, take him to these stages. (except delfino, he gets low % up kills there a LOT.
Overall, DK is a beast. He can take a beating and survive well into the 200% range if you DI well. He doesn't match up poorly against much of anyone other than Snake, DDD, and probably Falco. I'm not saying he's got the advantage in the other matchups, but if you can't overcome 60-40 with a relatively underused character outside of nationals, you should just play Metaknight anyways.
edit: I forgot throws!
DK's grab has rather good range. His options after grab are pretty good. At low %s, cargo carrying people isn't really an option, since they will struggle free very quickly. I haven't worked a whole lot on grab release tactics, but I'm sure OS or someone can find some tricks there. Maybe cargo -> grab release -> Nair would work well.
Cargo spiking is an option against most people you play against, who won't be able to time the techs all that well. I've cargo spiked pretty good players in tournaments before, so no one is immune to it. Even if they don't get hit so far downwards that they couldnt' recover, if you spam jump as soon as you throw back into the stage you will usually get a footstool, which is enough to kill most of the cast, often including metaknight. (depends on the stage, and the %)
After a grab at middle %s, cargo for just a moment and forward throw. It will throw them at a low projectory off the stage. This sets them up perfectly for a Dair or Fair spike. I use this much more than cargo spiking, as it is much more reliable at lower %s.
Back throw is a killer at high %s, or on stages with narrow sides. On Jungle japes, you can grab on either side platform and back throw off the side at pretty low %s. The same is true on any narrow sided stage, or on walkoffs, if you are brave.
Up throw can be used to set up Uair, but I don't use it much, since I usually have better options from grab.
Down throw is not bad either, dealing a decent amount of damage. I use this at low %s since I won't expect to get a good chance to set up a spike before they struggle free, and I THINK Down throw is the highest damage of any throw DK has.