The multiplayer is generally shit, because (unlike Demon Souls) Dark Souls didn't get a dedicated server, so don't expect a lot from it. Often, when you -do- finally see a summon sign, the summoning will fail. 
If you want to do multiplayer co-op, the best bet is to go to the Steam forums. Get a mod for Dark Souls that allows you to connect to friends more easily (also, get some friends for the game) and read a couple threads that give you tips about the online stuff (e.g. you -don't- want to restart the game in hopes it helps your connection, that actually hurts the chance you'll find someone do to the way the IP pool works).

If you see a player enemy, there's a large number of them (on the PC) that are hacked to be overpowered and still able to invade you. Those players will be literally impossible to beat. In the case you want to be certain you don't lose anything, it's best to close(/exit?) the game really fast, or turn off whatever you're using to play it. 

Read the stuff you see, don't skip it, and try to pay attention to detail. It usually matters. You'll get rewarded more and punished less that way.
Leveling up is not the only way to beat the game. A lot of the game is 1) Equipment, and 2) Knowing what you're doing. There are people who can play through the whole thing, all on Level 1.
If you're stuck, ask the Internet, or look up the wiki. That'll help a lot for number 2.

There's a lot more. I guess I'll just add:
Equipment weight matters for dodging, speed, and (as I recall) stamina.
Don't piss off useful NPC's, or they're useless for good.