Dark Souls is way harder than Demon Souls.
Having played Demon Souls it helped, but wasn't enough to be "good" in Dark Souls.
Taurus Demon on the bridge: As soon as you come out of the white into the fight with him, run down the little stairs and turn right. There's a ladder that goes up on the tower you came out of. Use that to jump down to attack the demon. Massive damage.
As for the rest, just play and get souls. Level your character up and get some good armor/weapons. The Drake sword is nice and very easy to get, just takes a lot of arrows.
Once you understand the controls you're good to go.
Just remember, block first, attack second. Once you can parry and counter you'll be murdering everything.
Once you're high enough, you can just run around and 2H kill everything lol, that just takes a while.