Essentially PvP/ Co-Op in Dark souls is based on Level. Say your level 20 you will only find people approximately (This is arguable as no one truly knows the level cap) 10 levels away from yourself so 10 - 30 (some people believe it is 10% your level so 18-22).
(You have to be human to invade/ be invaded unless your in a covenant)
PvP is set as invasion (so you may be playing and someone might join you). The enemy will not be attacked by enemies on the map and has complete freedom in the area your invaded in (I believe you cant escape other than quiting.
There are several ways to be invaded/ invade, most common one is however covenant territory (Darkroot garden is PvPPPPP territory as you can get more than one invader). Others include covenant specific items which search for a person to invade.
Covenants only allow you to invade someone higher than you are (I don't think theres a level cap as I've been invaded by essentially level 1's while I was high 100's)
PvP is somewhat laggy but tolerable to an extent you will very likely get lag stabbed in the back but don't let that deter you to much as you are playing people across the world (no region specific servers)
I think that covers the base of PvP, its great fun once you start getting into it plus if your set up/ strong enough you can be almost unstoppable
Use this also as a guide for PvP/ CooP level. It will give you some idea at what level you should be where and when (to low and you won't see anyone other than griefers who rush the game to get high end gear and essentially rape low lvl players)
Also DON'T use Snuggly or any save editor if your going to be doing PvP. Don't wreck online for this amazing game so you can be be a bitch and have max op stats (don't take this personal its just a general statement to everyone who plays online Dark Souls)