Tip 1: Do not hit NPCs. They will fight back, and remain hostile until you manage to get through your first major boss test to talk to the NPC who can put them back on good terms for you, and doing so becomes increasingly expensive as you gain levels. Also, do not attack that NPC, because then you won't be able to make up with ANYONE you piss off.
Addendum to Tip 1: Do not hit breakable objects with your weapon--learn to roll through them instead.
Tip 2: Playstyle is more important than stats. There are many weapons that are powerful in this game, but far more important than the damage you can inflict with a weapon is your comfort level when handling it. By all means, upgrade a weapon you like, but test its moveset, learn its strengths and weaknesses, and decide whether or not you want to stick with it or jump to something that handles better, rather than saying "Oh this deals more damage so I guess I should upgrade."
Addendum to Tip 2: Weight has a major influence on playstyle. Do you want to be swift and agile, or poised and tanky? The three major weight brackets in relation to your equipment burden are "below 25%" (known as fast roll territory), "26-50%", and 50%+ (also known as fat roll territory). For beginners, the middle ground is usually best for general purpose. If you find you like dodge rolling frequently, you may want to consider lowering your equipment load so you can roll faster and dodge more.
Tip 3: Resistance is futile useless. Do not invest stats in it unless you have absolutely nothing else worth ranking (ie. all other stats capped).
Tip 4: Environmental cues are all around you. All items you find that are not drops from enemies will always be around a corpse of some kind. Ask yourself how that corpse got there before rushing in and grabbing it, and you may find yourself living longer. Furthermore, pay close attention as you wander into new areas. Environmental traps and ambushes can be detected if you just look (and listen) before you leap. Also, you can use various parts of your environment to your advantage.
Tip 5: Always be prepared for a boss fight if you walk through a fog door. Not all fog doors have a boss behind them, but every boss you will face is behind a fog door. This will save you some grief because some bosses will be on you the minute you enter their domain, with no chance for getting your bearings.
Tip 6: Study enemy attack patterns, learn what can or cannot be punished, and how to punish it. You'll be tempted to backstab everything you fight early on, but knowing when to block, kick, parry, and roll can be just as important to your progression. Also learning what can be baited and how will open up more opportunities to punish.
Tip 7: Death is always around you. You will die eventually. Sometimes, that death will be at an inconvenient time in a very inconvenient place. You can lessen the inconveniences if you have better control over where and how you die. If Estus is getting low, stay along paths that are easier to get to in anticipation of a return trip from the bonfire, rather than in the middle of a field of enemies. Keep boss fights within range of the fog door if you can help it, so that soul retrieval is easier to manage when you get back.
Tip 8: Anything goes. Snipe that annoying S.O.B. with poison arrows. Run past enemies if you don't feel like fighting them. Lure that one idiot over a cliff (hell, KICK him over the cliff if it helps). Cast spells, fling fire bombs, use resins, run naked. Whatever gets the job done. If it can be done in-game and it's not a hack, it's fair game.
Tip 9: If it's a boss and it has a tail, you can usually cut the tail, especially if said boss is draconic. Several bosses will give you nifty items for mangling their tail. Some of these are good, many of these are crap. But, if you're a completionist, it's always a good idea to pay attention to a boss with a long tail. Not all tailed bosses can have their tails cut, and a boss or two might not give an item even if their tail is able to be cut. Now if you'll excuse me, I need to try for the nth time to cut Kalameet's tail while not having fast roll.