Hehe I knew this was coming soon...
The quick keys menu is F1. You can see all the keys (and change them) in Esc > "Options".
To "swing" or attack just left-click (not right- like in Arena and Daggerfall) with the mouse, while your weapon is drawn. There are three types of attack, "chop" "slash" and "thrust" I think. By default you choose the attack by moving the mouse in a particular way while clicking, only that there's only one correct attack for each weapon. For example a chitin spear does up to 13 damage with "thrust", but only up to 2 with the other attacks. As Darth says there's an option in the menu (again Esc > "options") to always use the best attack for every weapon, and then attacking is just click-click-click.
If you hold the left mouse button pressed a little the attack will be stronger. (You can press tab to switch to third person for a moment and see how long does it take your character to wind up the strike completely.)
The best way to collect money is looting of course. But for now I'd just see what you can do in Seyda Neen and then follow the story at least until you're in Balmora. There you can join any guild (and the Imperial cult in the fort outside town) and get quests to level up.
When you're starting out you can make a difference in money by stealing everything you can, if you want. You don't need a good stealth skill if you can find places where nobody's looking, although it's good to use those skills to train them. And remember that you can't sell something if you stole it in the same store/house, because they will recognize the stuff.
Alchemy can be a source of income too, as you can find ingredients everywhere. You can sell them directly but the potions should sell for much more. Also alchemy is hugely useful in Morrowind. You'll need at least a mortar, you can buy or steal one at a number of places, for example the Mague's Guild.