Satangel is absolutely correct. We cannot stress the quicksave option enough. It should become as common as breathing. You should save before you walk through most doors, and any time you're about to pickpocket or steal something risky.
TES games
have lots of bugs develop random features of awesomeness, some of which are so awesome that the game is incapable of showing them to you, causing it to faint from excitement.
The rest of my recommendations have no basis apart from how I have played Morrowind and Oblivion.
Join the Mages and Thieves guilds.
Jump everywhere you go. And fall off of things. If you live, it's quite helpful. Hope you saved before you jumped, though.
^ Acrobatics have been removed from Skyrim
Shiny thing? Steal that shit.
^ Just be sure you can use it yourself, or you can sell it to a fence, or you have a house you can store it until you can find a fence. For the love of all that is good and holy do NOT place items in containers that do not belong to you. They may stay there for a good while, but when the game decides to refresh that area, you are going to lose your stuff.
Destruction and Restoration skills are must-haves for all travelers. I also recommend alchemy, but it's rather tedious.
Somewhere in the game you'll find a lockpick that you can't break. Jump through
any hoop you have to in order to get it.
^ Without giving away many spoilers, you get some pretty neat perks for returning said lock pick. Just be sure to use it as much as you can before then, because you can't get it back.
Main quest? There's time for that some other day. (500 hours of Morrowind. Never completed the main quest)
ENCHANTMENT! First thing you enchant is a sword with soul trap. (1 second, on strike) Gather up as many soul gems as you can get, then start using the sword to fill them up, and then go make even more enchanted items. At the very least they sell for a pretty penny, and if you stole the soulgem that you used in the enchantment your profit margin is even higher.
^ Conjuration has a perk that you can attain for conjured weapons that automatically cast soul trap with every hit. Very helpful.
If at any point you find yourself hacking through a deep, labyrinthine dungeon with many levels, and you weren't sent there by a quest: turn around. You're about to screw up a future quest.
^ Skyrim is pretty forgiving with this. If you retrieve an item from a quest, you can just hand it in right there during the quest acceptance dialog. There is even dialog specifically for that. Others, you need special items to even continue, so all in all it's kind of hard to screw up future quests.
When in doubt:
UESP.