Don't get greedy. This is the golden rule of Dark Souls, and the key to your success or failure playing it.
Story-wise, the game is deceptively simple. At first appearance there is little information given, you are told almost nothing and given a surprisingly large world to fight in. But this is what a lot of people love about Dark Souls - you get out of it what you put into it. Dig a little bit below the surface and there is actually a vast lore with tons of information, detective work and speculation for you to piece together if you are perceptive and observant. Item descriptions tell an entire world's worth of details, occasional lines of NPC small talk reveal facts that can expand the lore by surprising amounts, details in the landscape give inferences to greater world events. The only times you are directly told something important you can be sure as hell the tellers have an angle they are pushing and it probably isn't the full picture.
World design-wise, you have a surprisingly large stage to explore and, most importantly, it *feels* like you are exploring a massive land in a fading world rather than a set of different levels. Just about everywhere in the game is interconnected and criss-crosses with other areas in some way, you can walk from one area to another and then look back and see exactly where you came from and look forwards and know you'll eventually get there (and sometimes even see tiny orange player messages in the distance, which is a nice touch). The shortcuts exemplify this, it genuinely feels like everything is one large castle.
Mechanics-wise, see the first sentence. This is a game of patience and cat-and-mouse baiting. Lure enemies into one-on-one combat, don't get flanked, learn when to tank and when to evade, plan your attack movements, use everything and anything to your advantage. Death has little meaning as everything lost on death can be infinitely regained, so it becomes a learning mechanism rather than a punishment. Sometimes the lesson may be 'go elsewhere' or 'try a different method.'
Character building can vary greatly. Do you want to be a heavy knight with a massive weapon, or a dexterous archer, or a tactical mage? The beginning class choice is essentially meaningless in the long run, it just determines what gear you start with and gives you some stats you'd have even with a different class (eg you'll probably end up putting some points into faith so for the heal miracle regardless of your build). You can effectively beat the game with almost any playstyle or build, though some are definitely easier than others.
Use humanity at a bonfire to un-hollow yourself and you can summon other players to help you fight areas and bosses at the risk of being invaded and killed by someone else. There are also NPCs who can be summoned and even invade you, which is nice if you're offline, though there are sometimes conditions for summoning them such as them having been in the previous boss fight or them invading you and defeating them.
There are some spots it suffers from poor design, let's be honest. These are generally not so much in terms of enemies or player options but in terms of terrain and meshes - the Great Hollow is a good example of this, sometimes you will go flying down and to the side to your death because god forbid you touched the wrong angled mesh despite having had an apparently clear angle to your destination. The Bed of Chaos is especially obnoxious with this, but the less said about that the better. The Painted World doesn't mesh with the rest of the game very well, it's more or less where the devs put half-finished ideas that they didn't want to throw out, which is a pity because information on the stage itself and boss are very interesting but rather undeveloped and could have been expanded on much more (I was especially disappointed that I couldn't return the doll to its owner). Most of the game has excellent level design, however, the exceptions to this are only exceptions and not the rule.
I am not skilled enough at pvp to really go into it, look elsewhere for an analysis on that. I will say that in my experience pvp has been annoyingly full of longer-range bleed weapons and little else in terms of variety, lag is also very much present and will lead to you missing when you clearly connected and getting hit or backstabbed when you were clear across the area.
All in all, brilliant game that you will probably quit the first time you play it then come back to much later and eventually enjoy. Takes time to 'get it' which can be considered both a major weakness of it and a massive strength to it. Just about every bit of progress you've made (both in-game and in understanding/learning the game) is a result of your own effort and accomplishment, very little is given to you so again you get out of it what you put into it.
Note that due to the devs self-admittedly being inexperienced at PC porting, there are some native issues. These are mostly fixed by getting DSfix and configuring it for whatever needs to be tweaked for your setup.