First you must understand you UO itself is... Its a "massively multiplayer" game. That means that there are thousands of players on at once, unlike in SC where there can only be up to 8 players in a single game. The game is set in a medieval setting, and is rather realistic.

I'll explain the skill system first:
There are a total of, I think, 54 skills in the game.You can start with 3 skills in Ultima Online, and you have 100 points to distribute amungst them. The most skill points you can ever have are 700, that means you can only become a GrandMaster *have 100 points in a skill* for 7 skills, or you can GM in less and have a few skills that are only at apprentice *50-59* or so skill level. You gain skill points the more you use the skill, like in real life. You usually gain at 0.1 at a time, but you can gain up to .5, but either way becoming a GM means a LOT of work.

For combat skills, your skill is automatically checked each time you use a weapon, and it judges the effectiveness of that with a random number generator. I'll explain the main combat skills:
Swordsmanship: This skill is checked whenever you usea sword, or any axe other than a war axe, wich is a mace weapon *see below*.
MaceFighting: This skill is checked whenever you use a mace weapon, wich is any blunt-ended weapon *clubs, maces,etc...*
Archery: This skill is checked whenever you use a ranged weapon.
Fencing: This skill is checked whenever you use a fencing weapon(all knives, daggers, and the kyrss). This skill allows you to block enemy attacks while attacking yourself.
Wrestling: This skill is checked whenever you fight unarmed.
Parrying: This skill is checked whenever you use a shield. It gives you a chance to block any incoming attacks.

Those are all of the combat skills. I use archery, my main skill, then swordsmanship, parrying, and fencing as my other skills.

I will explain the "stats" now. There are 3 stats, strength *str* dexterity *dex* and intelligence *int*.

You can have a maximum of 225 stat points, each stat can have up to 100.

STR decides how much weight your character can carry, what weapons your character can wield, and how many hit points you have, with the maximum being 100.
INT decides how much mana *spell points, akin to mana in SC and WC* you have. The more INT you have the more mana, wich is necisarry for casting spells.
DEX decides how fast your character moves, and mainly, most importantly, what your rate of attack is in archery. This stats raise depending on what skills you use, and how much you use them.

Last thing for now is that almost all characters are unique. You can choose from DOZENS of skin tones, DOZENS of hair colours, several hair styles, facial hair styles, and you can be male or female.

Here is an example story of skill gain:
You attack an ettin. You hit it: Your skill in archery has gone up by 0.2, it is now 54.3. Your skill in tactics has gone up by 0.1, it is now 67.4; that is how your skill goes up. Ok here is an actual story type thing:
An ettin suddenly burst from the trees near the young woodsman, and was immediately hit with several arrows from the young archer. The young man could see his shots becomming more and more accurate as he attacked, and knew he was becomming more dexterous *I think that is actually a word, not sure heh*. Soon the beast began to flee, as it was severly injured. The young man pulled a longsword free from its sheath on his back, and charged the beast, he attacked, and knew that he was becomming an adept swordsman, as he dodged the clumby attepts of his foe to block his attacks, and parried the beasts attacks with his kite shield. Soon the beast was slain, and for slaying such a massive and evil beast, he gained much fame and karma *check UO Straitcs for information on fame and karma*.

I hope that this helped you gain an understanding of the game mechanics of Ultima Online.