I'm going to try and update with things as I find them out and hopefully provide some useful info.
How to start: Hit "H" to bring up your Hero tab. Click on the Crossed-Swords Icon at the bottom of the left tab. Click on "Enter the Mists" button.
A brief tutorial shows how to revive downed allies, finish enemies, and how to capture a point. This is only required to progress 1 time. Any alt will not see this area.
What's the difference with my character?
Characters in the Mists are set at max level. You have access to all Skills and Traits. You are given a default build, but can respec anything you like whenever you like. Take some time to look at all the abilities.
How to build my character?
There are a few guides out already, and surely more to come. The general concensus is to build around your playstyle, and to specialize. But most importantly try to pick skills and abilities that will synergize with your weapon selections.
How do I equip my character?
Your character starts with default weapons and armor. You can change your weapon types by access a vendor. All of this is free. PvP lockers will store weapons/equipment currently not in use.
How do I get better gear?
Good news! You already have the best. New gear will be unlocked as you continue to PvP, but they will only confer cosmetic benefits. GW2 is skill vs. skill alone.
What else can I do in this area?
There are training grounds so you can check out the different Battlefields. Its good if you want to get a lay of the land. The tournament access is also here.
How do I leave?
Exit the area the same way you entered, through the Hero PvP Tab.
I've got new cool looking gear, but its got an Unused Upgrade Slot. How do I fill it?
Both the Weapons Vendor and the Armor Vendor have a seperate tab where you can purchase "Enchantments" that you can apply to their respective equipment. Weapon Runes are one-off enchantments that provide a variety of effects. Armor Runes are parts of sets, so you want to either pick an entire set that has bonus stats you like or mix-and-match to get the bonuses you want. All this can be done with 0 costs.
Ack! I've gotten multiple copies of the PvP rewards. Do I just destroy them?
Yes, but not how you're thinking. You can purchase PvP Salvage kits and breakdown any duplicate PvP items you get in rewards chests. From there you can visit the Mystic Forge (located just North of the Vendors in the Mists) and combine the materials for a chance at new equipment.