To understand the jargon in Baldur's Gate, it helps to visualize what people do when they play D&D on paper. First of all, they roll dice for a variety of things. When I say dice, you might picture two cubes with six sides and dots on each side ranging from one to six, but those are merely six-sided dice. If you really want to see the fun in pen-and-paper D&D, picture twenty-sided dice.
There are also four-sided dice, eight-sided dice, and ten-sided dice.
Let's start out simple. If you have a Fighter, he gets 1 to 10 hit points per level, up to 9th Level, plus a Constitution bonus (we'll get to that later). In Baldur's Gate, he automatically starts out with maximum hit points. But from then on, when he levels up, the computer "rolls a ten-sided die" to determine how many extra hit points he gets. If you were playing pen-and-paper D&D, you would actually roll a ten-sided die. The Constitution bonus is a number you add to each "hit die" if your character has an exceptionally high Constitution. For example, if your character's Constitution is 18, he gets four bonus points for each hit die. Instead of only getting 1 to 10 hit points per level, he gets 5 to 14 hit points per level.
The heart of the D&D combat system is the twenty-sided die. When you try to hit a monster, you have to roll a twenty-sided die to see if you got a hit. Your chance of success is determined by: 1) your character's THAC0 (which uses Armor Class 0 as a reference), and 2) the monster's Armor Class (or AC for short). For example, suppose a monster has AC 0 and your character has a THAC0 ("to hit Armor Class 0") of 15. That means you need to roll a 15 or higher on a twenty-sided die to hit the monster. Anything less than 15 results in a miss. (Back in the old days, if you rolled a 1, which is called a "critical miss", your character actually hit himself with his own weapon. Even today, a natural 20--a 20 rolled without any bonuses--is called a "critical hit" and does double damage.) Now here's where it gets complicated. Suppose a monster has AC -4 (which is four points better than AC 0). You have to add four points to your character's THAC0 to see what you need to roll for a successful hit. If you start with THAC0 15 and add four points to hit AC -4, then that means you need to roll a 19 or better to hit the monster. Anything less than 19 results in a miss. Anything better than AC -5 would be almost impossible to hit, although I think that "natural 20" hits any AC--I don't remember for sure.
A human with no AC bonuses has a base Armor Class of 10. (A character who has THAC0 15 only needs to roll a 5 or better to hit a character who has AC 10, see?) Leather armor is worth two points, so a character wearing leather armor without any other AC bonuses would have AC 8. See how that works? Characters who have exceptionally high Dexterity get AC bonuses. For example, a character who has Dexterity 18 gets four bonus points, for a base AC of 6. Better armor, Rings of Protection, and Dexterity bonuses can give a character a pretty good Armor Class. In BG2:Shadows of Amn, the game does not recognize anything lower than AC -10, but it's hard to get an AC that good without cheating.
Back on the subject of hit dice, monsters have a predetermined number of hit dice rather than "levels", but hit dice are kind of like levels. A 4th Level Mage has four hit dice. I think a troll has six hit dice, or maybe it's more. When you see references to "hit dice" in your spell descriptions, that's what it's referring to. Some monsters won't be affected by the lower level spells or even some of the higher level spells. Dragons have over twenty hit dice.
Learning spells and memorizing spells are two different things. To add new spells to your character's spellbook, you need to "write" them into your spellbook by reading a scroll. In order to cast spells, you have to "memorize" them once a day. Click on the icon for your spellbook on the left side of your screen, then click on the spells you want to memorize for the day. The spells you memorize are the only ones you can use that day. To memorize new spells, you have to rest. You can rest as often as you like, even more than once in one day. (The game will tell you that you've been sleeping for eight hours.)
Unfortunately, your characters can't swap spells. In the Baldur's Gate series, a Mage has to find or buy scrolls with the spells you want to put in his spellbook; there's no other way to acquire them. Sometimes monsters drop scrolls, sometimes they're in locked chests, and sometimes you can buy them from a store or a street vendor.
On the other hand, if your character is a Cleric or a Druid, he or she learns new spells automatically when he or she advances in level. For example, as soon as Jaheira is able to use 5th Level spells, ALL of the ones she can use automatically appear in her spellbook. Don't bother looking for other spells for her to use; it doesn't work that way.
As Bloodstalker said, you need to be aware that Specialist Mages cannot use spells from their opposition school(s). For example, a Conjurer can't cast Identify, which is from the opposition school, Divination. Whatever you do, don't play a Transmuter. They can't cast spells from the school of Abjuration, which makes them virtually helpless.
You know what I really think? I think you should play Baldur's Gate (the original PC game) before you play BG2: Shadows of Amn. That's the best way to learn how to play. Things are a lot simpler and a lot easier to learn in BG1, and besides, it's a really good game.
Good luck!