EVE Online | Player Guide
Couldn't find the one on Sov.
Basically, you have to have Sovereignty in a system (POS majority; larges count of mediums, mediums over smalls). Things are a little more complicated with the new capitals and constellation sovereignty. For the most part, POS's take a week to start counting towards sovereignty (and they have to be set to do so). An attacker can neutralize sov by killing the enemy POS's in system to match the amount of POS's they have claiming sov in system or putting down more to match theirs (a limit of 5 per corp per day was implemented).
If you're shooting POS's, basically they're like a big ship. You fit them with hardeners, webs, scrams, guns, like you do a ship. You can now shoot the offensive modules of a POS and incapacitate them. They need 1 point of structure damage to be incapacitated. POS's are fueled by ice materials and need to be refueled about once a month. Because POS's claim sov and due to time differences, CCP implemented a "reinforced mode" on POS's in which they are invulnerable when they reach 25% for some time. This time is set by the amount of stront put in it's storage bays. When the POS gets below 50%, the amount of stront cannot be changed. When in reinforced mode, the POS will show a timer indicating how much time is left. When the POS comes out of reinforced, it is again vulnerable to attack and it can be destroyed. Once it's destroyed any anchored modules may be scooped by the attackers.
Once sov is neutral (all sov changes happen over daily downtime), you can shoot the station. Once the shields go down on the station the last player's corp that shot it gains control of the station. After that the shields will regen slowly over a few days or you can repair them if you like.
As of Rev3 you can also shoot station services. You can take out the fitting, clone, factory, repair, etc slots making those that have access to the station unable to perform those tasks. Much like shooting POS modules, most of the HP of the services is in their shields, removing the armor and shields will incapacitate the service.
That's the basics, I'll see if I can find that sov article.
