Alchemy's main perk is the Mixology buff, which provides an increased effect and duration when you drink an elixir or flask you can create. For flasks, that means an extra 320 strength from Flask of Winter's Bite or an extra 480 stamina from Flask of the Earth. When you don't want to waste a consumable, you can also use the Alchemist's Flask, which is not consumed and offers a smoother 320 strength boost at level 90. This makes it great for DPS, and at least passable for tanks, who get some extra threat and parry rating from it. You can also get the Zen Alchemist Stone, which is only item level 450, but offers a nice stop gap until you can get heroic dungeon trinkets or better.
In addition, the ability to personally create Living Steel can be helpful when trying to get someone to make you blacksmithed armor or weapons, as most high level stuff will need a few bars.
Blacksmith's big draw is still the extra sockets. You can create an extra socket on your own bracers and gloves, which, while expensive to fill, gives you an opportunity for more stats. An added bonus here is that gems are not limited to primary stats, which means tanks can choose to gem for mastery instead of stamina.
Blacksmiths also have the advantage of being able to create their own weapons and armor. If you don't mind a little farming, you can build heroic dungeon and LFR level weapons and armor to give you a leg up on normal, such as Masterwork Spiritblade Decimator. Note that all of these are bind on equip, so you can just buy them, but they may be more convenient to aquire if you're a blacksmith.
Enchanters can enchant their rings for a combined 320 strength or 480 stamina, making the bonus competitive with any other single primary profession. Other than that, you'll have the convenience of being able to do your own enchantments.
Engineers get Synapse Springs, which will proc strength for us, and Phase Fingers, which proc dodge rating. You can either use them strategically as you need burst damage or defense, or make a macro that ties the line "/use 10" (10 being your glove slot) to a commonly used button such as your runic power dump. Note that you can still throw a glove enchantment on top of these as well, so don't skimp.
Engineering also gets cool toys like the Goblin Glider and Nitro Boosts, which may provide specific utility for certain dungeons and boss encounters. Get thrown in the air or accidentally fall off a cliff or elevator? Use Goblin Glider or Flexweave Underlay to survive the fall. They also get Ghost Iron Dragonling, which can be helpful for getting them into heroic dungeons, and Reinforced Retinal Armor, which aren't quite as good as normal raid gear, but will offer a nice gear boost for those not in a raid or for those whose helm hasn't dropped yet.
Herbalism still gets their self-heal Lifeblood, which also provides a haste proc. If you use it on cooldown, it evens out to about 480 haste. It's not the greatest, but haste is still a pretty solid stat for DPS, and if you're a herbalist, you'll want to make sure you use it.
Inscription can use super powerful self-only shoulder enchants, including Secret Tiger Fang Inscription and Secret Ox Horn Inscription. Now that shoulder enchants can't be purchased from NPC vendors, it may be even more convenient to be able to make them yourself.
Jewelcrafters can make Bold Serpent's Eyes and Solid Serpent's Eyes, and socket up to 2 for an extra boost of stats. If there's a big disadvantage here, it's that heroic dungeon gear no longer has many sockets as a rule, so you may have to wait for raid gear before getting the full benefit of the stat. Tanks, while you might be tempted to make some Fractured Serpents Eyes here, note that as of this writing, Solid Serpents Eyes will probably give you more staying power as a tank all else being equal.
Leatherworkers get Fur Lining - Strength or Fur Lining - Stamina. Since there's not a major stamina bracer enchantment, that 750 stamina makes leatherworking a sleeper hit for tank death knights.
Mining gets a bonus of 480 stamina at level 90, making it a pretty passable choice for tanks. DPS won't get as much use of the bonus here, but even DPS are in a pickle when their health reaches 0, so it's not completely useless.
Skinners get an innate bonus of 480 critical strike rating. Critical strike isn't a top tier secondary stat for any death knight spec, which makes this skill a little lackluster. If you're taking this, take it for the money selling skins or to supply a leatherworker, not for the bonus.
Tailoring provides cloak enchants. Swordguard Embroidery offers the ability to proc a burst of attack power. This makes it somewhat passable for DPS, though tanks still have no option that directly affects their survivability.
One other reason to take tailoring, though, is if you're a bag space junkie. The only new bag recipe in Mists requires 12 Imperial Silks, which are BoP and can only be created either once a day or via the use of Spirits of Harmony. If you want the bags, having a main character who has 600 tailoring may be the best way.
A note on choosing your professions
For the most part, you can choose your professions with the knowledge they won't really gimp your playstyle. Primary professions have a large enough stat boost from their self-only abilities that you'll almost never be "behind" another profession. Gathering professions lag behind a bit, but you still get some benefit. Choose what professions sound interesting to you, use them regularly, and won't be going too wrong. Don't worry if you like picking flowers. Real death knights totally pick flowers.
If you absolutely want to min-max, as a tank, you should probably try for a combination of leatherworking and blacksmithing. Blacksmithing gives you the flexibility of using stamina or mastery in the extra gem slots as needed, while the stamina fur lining for leatherworking more than outpaces the mastery bracer enchant you'd otherwise use. As DPS, your main focus is taking two professions that provide 320 strength, which is basically every primary non-gathering profession. Even the engineer's proc evens out to about 320 strength in the long run if you use it consistently. My personal preference is engineering, since the option to use your bonus as a bit of burst defense or damage and the added toys add some variety to your gameplay, but again, there's not really a wrong choice here.
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.