Everyone always asks which gems they should put in their new gear. I'm going to answer that question in a simple and easy way here.
DPS Gems
In every slot possible, socket pure Strength gems. It doesn't matter if you'll get the socket bonus or not - socket Strength. The only time you wouldn't do a red strength gem would be if the socket bonus plus a different gem (ie: +8 Strength, +12 Stamina in Blue socket with +8 Strength as bonus) gave equal to or more strength than 16. Another reason to socket something other than Strength is if you're trying to activate a meta gem. In this case, use a +8 Strength/+12 Stamina gem for a blue, and +8 Strength/+8 Crit for a yellow. The final reason to gem something other than Strength is if you're trying to hit a Hit or Expertise cap. In this case you may want to use pure hit (yellow) or expertise (red) gems. For a meta gem use +21 Critical Strike Rating (or +21 Agility) and +3% Critical Damage.
Tanking Gems
Death Knight tanks should, whenever possible, socket pure raw Stamina gems (blue). They may find that they need to socket Hit (yellow) or red (expertise), however, to meet caps for those stats. If low on Defense, a gem slot may have to be used for a Defense gem (yellow). For a meta gem, the Austere Earthsiege Diamond is definitely the best.
Enchants add so much to every class, as long as they choose the right ones. Here are the best gear enchants for new level 80 Death Knights to get, to help them on their way to epics.
Best Cheap(ish) DPS Enchants
Head - Arcanum of Torment. Sold by Knights of the Ebon Blade quartermaster. Requires Revered reputation.
Shoulders - Greater Inscription of the Axe. Requires Exalted Sons of Hodir Reputation.
Back - Major Agility
Chest - Super Stats
Bracers - Greater Assault
Gloves - Greater Assault
Belt - Add a gem slot to your belt with an Eternal Belt Buckle.
Legs - Icescale Leg Armor
Boots - Greater Assault
Weapon Runeforge - Rune of the Fallen Crusader
Best Cheap(ish) Tanking Enchants
Head - Arcanum of the Stalward Protector. Requires Revered with the Argent Crusade.
Shoulder - Greater Inscription of the Pinnacle. Requires Exalted with the Sons of Hodir.
Chest - Greater Defense or Super Stats, depending on what you need.
Cloak - Titanweave, Agility, or Armor, depending on need.
Bracer - Major Stamina
Gloves - Armsman
Belt - Add a gem socket with an Eternal Belt Buckle.
Legs - Frosthide Leg Armor
Boots - Greater Fortitude
Weapon Runeforge - Rune of the Stoneskin Gargoyle if you need the Defense, Rune of Swordshattering if not.