Step one: Build your own character
The best n00b combination is a Nord with Athletics as a major skill, and the Steed as your starsign. This combination will give you a very fast walk/run speed, and you will have enough strength to carry more loot before slowing. The greater percent of your max load you are carrying slows you down more. If you don't trust yourself to find the hidden weapons around the starting town, make sure you take shortblade as a major skill, because the tutorial hands you a dagger. If you end up with only that dagger to defend yourself, the more impossible the game will be if your character doesn't know how to use it. Old ladies will literally beat you to death with their bare hands if you don't know how to use your weapons.
My personal build involves being a Bretton with the Atronach starsign, but you walk SO SLOW, have no strength to carry loot, and your weapon skills start really low, so battles are harder starting out. This doesn't deter me in the slightest, because those low skills mean they can grow more for getting to higher levels. I do not suggest this to a newbie player, but I point it out so that you know I'm not suggesting the above build because it's just the best for everyone for all situations.
Step two: Exploration
At first glance, you won't see many bad guys, but trust me, they are waiting just out of sight to rape you. Just jump in the water to see how fast you die from the fish. QUICKSAVE OFTEN! As stated before, mind your green Fatigue bar. EVERYTHING you do, yes, even menu-based skills all rely on dice rolls for success, and that green bar modifies that chance for success. If you try to pursuade someone to like you while you are panting and sweating everywhere, they won't like you. If you've spent all your energy jumping and running before fighting a rat, that rat will kill you. Thankfully, if you are aware enough, you can usually save and wait for a moment to recover without drawing agro from most enemies.
Step 3: Exploitation
I'll let you figure out how to break your own character, but if you're familiar with the leveling system in Oblivion, you will find it quite similar. The more skills you level, the better bonuses you get. Unlike Oblivion, you can keep earning those bonuses after your character is ready to level up, so long as you don't rest. Alchemy and Enchanting are both skills that any character can profit greatly off of, because you will always need potions which can be sold for money or drunk to save your life, and the enchanting system makes better mages out of fighter classes than actual mages.
You will find a few enemies in the game that allow you to talk to them, and 2 specific ones that allow you to shop with them. Those two carry more gold per day than any other merchant, and they will always buy at sell at the item's full value, and not a modified value based on your mercantile skill. One is a mudcrab that is in the middle-south of the world map among some small islands. I warn you because I killed him on two separate characters without knowing you could talk to him. If you loot a mudcrab that has booze on him, you know it's time to load your last save.
Be on the lookout for the Boots of Blinding Speed. They blind you, so the screen goes dark, but they fortify your speed attribute by 200 points. Your natural max is 100, so you can get up to 300 speed with those boots. If you can get even 1 second of 100% magicka resistance, you will be able to equip the boots and suffer no ill effects from wearing them. It's one reason why I like those Brettons so much, because they start with 50% resist. I can run around with a dim, but not black screen until I can get that extra 50% resist. After you get them, travel is a breeze.
Speaking of travel, there are 4 teleport spells that you can learn, and no one really describes them too well in-game. There are two "Intervention" spells that take you to the nearest church/temple (depending on the spell and religion associated with it). Think of it as part of a town portal scroll from Diablo. You can gather your loot and then jump back to town, even if you are massively over encumbered. The other two spells are called Mark and Recall. You can cast Mark anywhere, and when you cast Recall, you will teleport to the place you cast Mark. It's like the other half of the function of the Diablo town portal scroll.
You can not screw your character up in any permanent fashion. You find yourself hating your weapon type of choice? Start working on a new one or (cheat and[footnote]I consider buying skill levels cheating, but it's up to you to use it[/footnote]) buy some training for your new weapon of choice. The ONLY thing you can do that might make an OCD min/maxer cringe is your endurance attribute. Every time you level up, you get 1/10th your endurance's level in max HP. So at 50 endurance, you will gain 5 HP per level. This means you can end up with about half the HP your character could have had you been working on improving your endurance early on. The only skills that increase your endurance is Spears, Medium Armor, and Heavy Armor. You want to get 10 levels in all 3 combined for each level until you reach 100 endurance. That usually takes 10-14 character levels to complete. Spears are easy to level, because your skill XP levels up with each hit, not damage dealt. So if you can get away with beating an enemy with the spear instead of stabbing it, you can earn a lot more skill XP for doing practically nothing. Much of all that is moot though. My first character was a thief, and I didn't level up my endurance much at all, and I was still god-like by the time I did anything with the main quest. These are tips for the OCD mix/maxers.
Step four: don't despair
Some of the best things about Morrowind are also its worst things. Personally, I crave the classic RPG experience. The dice rolls make my character his own entity who is capable or incapable of things that I might demand of him. Play his strengths, because you're going to have a hard time if you don't. As time will go on, your character and your playstyle will start to converge and you will become an unstoppable god. Even your green fatigue bar will start to become more and more irrelevant the stronger your character gets. You will win fights effortlessly with zero fatigue once you are strong enough. The downside to all this is that players who are experienced in games like Oblivion see many familiar elements, but forget that Morrowind isn't an action game with RPG elements as Oblivion is. It's an action RPG, with strong emphasis on the RPG part.
The world is HUGE, so learn teleportation, or the locations that grant you fast travel (The big bugs known as Silt Striders are a popular form of transportation). Don't be afraid to dive into any caves or dungeons if you come across them. Just be sure to save often! If you get caught stealing, you can reclaim your lost loot from chests in prisons marked as "evidence", but I usually quick-load instead.
Lastly, don't forget there is a difficulty slider in the options menu that can be changed at any time to any degree. As a veteran, I like to slide it up the stronger my character gets, but you might want to slide it down a bit if you are too challenged at the start.
On a personal note, I just wanted to add that Morrowind is my favorite game ever. I've played hundreds of games from all different genres, and up until I played Morrowind, I could never choose a specific favorite. Morrowind changed that for me. If you can find even a fraction of the enjoyment I have had from it, you will have a great time. There are certainly things that are getting dated about it, but in the end, there is little I would change about it. With that said, I should add some mods
Step Five: Mods
I don't really suggest mods until you've familiarized yourself with what the vanilla expereince is, so you know what needs changing. There's mods that makes the combat system more like an action game, and less like a RPG. There's tweaks, graphical overhauls, rebalances, pretty much anything you might want.
For a full overhaul, I'd check this one out, since I've been following it for a while. It tries pretty hard to keep the vanilla experience intact while still making the game beautiful.
www.somethingfornobody.com/2011/morrowind-modding-guide/
The site is down at the moment, but they should be back up soon. I've found their host to be a bit spotty sometimes.
Official plugins made by Bethesda. Looks like Beth stopped hosting them, so I found this one.
http://morrowind.nexusmods.com/mods/searchresults/?cat=12
Lastly, this is the biggest improvement I'd recommend to anyone starting out. If you want to pick plants, you have to activate and open them like a chest, and then "loot" it. It's very tedious when done repeatedly, and thankfully, Oblivion improved on that process. This mod gives a much more Oblivion style approach to picking plants for your potions.
http://planetelderscrolls.gamespy.com/View.php?view=mods.detail&id=2212
Other than that, I can't think of anything that NEEDS improving. One thing many people have problems with is the cliff racers. I know there are some mods that remove them (too drastic change IMO), but I found the best was was to modify the enemy to give them a 300% weakness to lightning (or element of your choice) so that you can make cheap spells take them down when they swarm you. They do drop valuable loot though, so it is kinda cheating. Their feathers sell for a lot while not weighing much, and they can be used to make levitation potions. Silver lining in that storm cloud of death and annoyance I suppose.
One more thing that someone just reminded me of: Weapon durability. With all the missing you will be doing, you will find yourself wearing out your weapons quite quickly. A miss is still a hit as far as the game is concerned, but your skill makes it ping for 0 damage. I wish the sound effects reflected this better. Anyway, weapons that are low durability also deal less damage. That can be helpful because you can land more strikes to level up your skills more, but generally, it's not a good thing.