On Friday I posted about a fairly standard tanking rotation for Frost Death Knights, and I'd recommend at least glancing over that article first since I'll be referring to it a bit here. Death Knights produce threat by DPS, so the abilities that generate the most threat, with a couple exceptions, also generate the most DPS. There was a little controversy in the comments about another rotation that's gained some popularity, and if that rotation becomes a little more accepted I'll write up an article on it as well, but for now I'm focusing on the best-known Frost rotation that also, IMO, gives the best idea of how the class is intended to function.
I will note again that this rotation is helped immensely by having Glyph of Disease, which causes Pestilence to refresh your diseases on all targets. If you prefer not to use that, you'll have to add another Icy Touch > Plague Strike to refresh the diseases. It's very important to keep your diseases up! You may even want to look into an addon to help you track them if you don't have one already.
Again, your rotation will vary slightly depending on whether you're fighting a single target or AoEing. Frost is excellent for AoEs thanks to the high AoE damage of its signature 51-point ability, Howling Blast. I usually start off with Icy Touch > Plague Strike to get my diseases up, a Pestilence to spread the love around, Howling Blast, and then a Blood Strike to turn over that last Blood Rune. You want to make sure Frost Fever is up on everything before even bothering with Howling Blast. After that it's just a matter of hitting Howling Blast whenever it's available, Frost Strike to dump HP, Pestilence when you need to refresh diseases (or Icy Touch > Plague Strike > Pestilence if you're not glyphed for it), Obliterate whenever your runes are refreshed and Howling Blast is still on cooldown, and Blood Strike to flip Blood Runes. And be sure to take advantage of those Killing Machine and Freezing Fog/Rime procs! I generally skip Death and Decay when DPSing because I'd rather spend those runes on Howling Blast. You can try it if you really trust your tank, but I wouldn't recommend it with anything but a paladin or another DK, and not until they have a good tight hold on the group. It's a decent enough AoE DoT, but it does generate extra threat, relies on keeping the mobs standing in it, and at a whopping 1 of each Rune it's the most expensive ability in your arsenal.
On a single target, just as when tanking, you want to focus on Obliterate over Howling Blast unless you have a Freezing Fog/Rime proc. Killing Machine procs can be put to use with Frost Strikes unless Freezing Fog/Rime is up. Even on a single target, it's better to use Pestilence to refresh your diseases if you're glyphed for it.
The main differences between the Frost tanking and DPS rotations, beside the hopefully obvious difference that you're doing it in Blood Presence instead of Frost Presence, are the lack of Death and Decay, the lack of Rune Strike, and the lack of bothering with your mitigation cooldowns unless you really feel like popping Anti-Magic Shell (or as I call it, the Banshee Bubble) so you can keep standing in that Blizzard. Unbreakable Armor is also back to giving a Strength bonus, so it's still worth speccing into and using even for DPS. And pop a ghoul every so often! If Rune Strike does proc there's not much reason not to use it, but if you just dodged something that means you've gotten something's attention and you might want to throttle back for the tank to pick it up. For me it's extremely easy to switch between the two since they're so similar. Your biggest difference is going to be gearing, which is a subject for a whole 'nother post.
But before that, we'll be discussing something that's become a hot topic lately: How Not To PuG.