So you've made an account in DUST, you've gotten a feel for the battles, and you've applied to the venerated Kite Co. Couriers (you have haven't you...?) Now you're ready to engage in the EVE cross-linking that makes DUST more than just another Unreal Engine shooter. Well hold on to your space nuts, padré, because...
... most of it's not in the game yet.
Unfortunately, you're not going to be taking over the galaxy and building Kite Co. into the glorious empire it is destined to be... yet. What I will explain here is what you currently CAN do, and maybe some idea of the future of galactic warfare.
For this to make any sense, you need to understand some terms from EVE.
Corporations are player-created "guilds." The Giant Bomb corp in EVE is Kite Co. Trucking. In DUST, it's Kite Co. Couriers. These are separate entities.
Alliances are two or more Corporations in a formal pact. In EVE, they defend each other. In DUST, controlled territory benefits all corps in your alliance. Truckers and Couriers will almost certainly form an alliance once it makes sense to.
Factions are the four NPC "nations" in EVE - Gallente, Caldari, Minmitar, Amarr. You had to pick one when you made a character, which ultimately means nothing. An EVE corporation can choose to ally themselves with one of these factions and fight on their behalf.
Also, check your Starmap in DUST, or watch Patrick and Drew drill into it in the Quick Look. Every region, system, planet, and district on that map is a "real" place in EVE that pilots can fly to, interact with (depending), and take over (again depending). Over time, DUST will hopefully spread across this entire map, and this gives you an idea of the territory you can eventually fight over.
EVE players or entire Corporations can swear allegiance to one of the four NPC factions. This opens up the ability to capture inner systems (through control points) and fight members of the opposing faction in open world PVP. EVE players earn loyalty points for their actions here, which can be traded in a store for primo faction gear and equipment.
DUST players are intended to be mercenaries, and as such, do not sign on to a faction. The "Mercenary" tab in your mission finder is showing generated Factional Warfare battles you can join, and you'll notice you can join on either side. DUST players earn no loyalty points. DUST victories do allow EVE players to capture that territory little easier, but that's about it right now. This is also where EVE players can bomb with orbital strikes.
The eventual idea is that EVE corps will be able to open contracts with DUST corps to participate in these factional battles. The DUST corp's resources and reputation will thus be put on the line with every battle. But as it stands now, FW is a nothing more than great place for DUST players to get wrecked by corps that have been around since the beta.
Kite Co. Trucking is not involved in FW at this time, and likely won't be. They're busy enough with...
EVE corporations can declare war on any other EVE corporation at any time, even if the defending corp doesn't want a fight. Players in corporations at war become Kill on Sight without penalty. Kite Co. Trucking is usually fighting off some chucklefuck Corp of the Week™ out to get easy kills on new players. (Don't fret though, this is how Goonswarm started.)
As a DUST player, you can't help here. These battles all take place in space, and our valiant trucker comrades are on their own.
Likewise, there's no Corporate Warfare system in DUST at this time. A DUST corp can't declare war on another DUST corp. There is supposed to be an "arena" mode added soon where corps can fight and bet against each other, but not yet.
Not Yet, Not Yet... Well SHIT! What CAN I Do?
Planets, son! This is the "Corporation" tab on your battle finder, and is currently limited to the temperate (middle) planets in the Molden Health region. CCP will expand this to more regions and more planets over time - intent being that the planet's proximity to the sun will eventually put you on a lava or snow map with appropriate hazards.
I was going to write out a section for this, but CCP's own blogs explain it just as well as I could - meaning I can't be any less complex. So start here, and then the update here. If you have any questions, ask below.
The super high-level tl;dr version:
Planets are divided into districts. Each district can have a facility that generates a passive bonus for that planet only.
Any DUST corp can attack any district at any time. You don't need to own an adjacent district, or have a presence in Molden Heath at all.
Planetary battles are always Domination matches. Capture the gun turrets to kill the enemy carrier ship. 16 players per side.
- Clones are both spawn tickets and currency. 80 million ISK buys a "pack" of 150 clones. Every battle loses a minimum of 150 clones, regardless of how many players actually use up.
- Owned districts generate 80 clones every 24 hours - more with facility bonuses. You can move clones to other districts you own (or use them to attack enemy districts) at a cost. Clones you have no more space for are automatically sold for 100k ISK per to the corporate wallet.
Districts have a "reinforcement timer" to prevent players in other time zones from attacking while you're asleep. Say the timer is set for 6 PM. If someone commits to attacking, the battle will take place randomly between 6 PM and 7 PM the next day. Teams on both sides will need to be standing by for that hour. You can't change the timer on a district you capture until the next 24 hour cycle.
- DUST corps have no taxes like EVE corps do. That's what the "Donate" button is for. Don't donate more than you care about, but as you can see, shit's 'spensive.
That's pretty much Planetary Conquest. There's more to it, like earning loot and extra clones for winning battles, and the bonuses to EVE players, but this is the basic idea. You'll throw a lot of money around, probably won't hold onto a district for very long, but it gives you something to fight for.
And should we manage to own all districts on a planet, well, two words: Planet Luchadeer.