Skills and Spells
Every even level (except level 2) you gain new skills and spells that can be bought from class trainers. These cost money, generally a rather hefty amount for your level, which can leave you poor. I recommend only buying what you know you're going to be using, or only buying the high level rank later on. This is because you can skip Rank 1 but buy Rank 3 when it becomes available, and so on. Skilling up weapons, tradeskills, and defense is different. Every time you level up, your skill cap is raised by 5. What this means is, let's say you start with 1/10 skill in maces and 1/10 skill in defense at level 1. As you use maces and get hit, your skill will level up. Let's say right before you level up, you have 10/10 maces and 10/10 defense. You hit level two, and your skills increase to 10/15. As you fight, it'll go up to 15/15 again. Then level three, 15/20. Get it? The higher up it goes the slower it raises. Note that you need more skill to be able to hit things. So if you're level 20, you'll rarely hit monsters your level if you have 30 skill in maces. And even when you do hit, it will be for single digit damage. If you have your skill maxed, you'll hit often and for alot.
Weapon Specialization is different still. Let's say you're a Warrior, and want to get the ability to use Guns. Well, you have to go to one of the major cities (in this case it's the Undercity) and talk to the Weapon Master NPC. For a cost, he'll train you in Guns. But when you get a new weapon or armor specialization, your skill starts off at 1/yyy, corresponding to whatever your level is.
Tradeskill leveling works on the same XXX/YYY system, but you have to use higher level skills to raise it after a while. Let's say you have Herbalism. Now, at level 1 you can collect Silverleaf and Peacebloom until you hit 15, then you can also get Earthroot. At 50 skill, Silverleaf will rarely, if ever, raise your skill. Earthroot will, but not as much. However, level 50 Mageroyal will raise it every time. (Until you hit the 100's, of course..)
Go to
Thottbot to see how you progress in skills every even level. Go to classes and pick one, then scroll down the list and such.
Talents
Talents work similarly to the Diablo 2 skill system. There are three talent trees per class. Depending on which tree(s) you specialize in, you can gain different abilities, and in some cases even become drastically different than someone who specialized in different talents. Note that some abilities such as Mind Flay for shadow priests can only be gained through talents. However, once you have them, they tend to level up just as other skills/spells do, meaning once you're the right level you can buy Rank 2, 3, etc from your trainer.
At level 10 and for every thereafter, you get one (1) [uno] talent point. You have to work your way down the talent trees to get to what are generally the more powerful talents. There are six steps in each tree, the top one needing 0 points in that tree to get talents, the next one needing 5, then 10, then 15, then 20, then 25, and finally 30 for the ultimate one. Also, some talents need prerequisite talents to invest in. Since it takes 30 points in a tree to get the last ability, making the total 31, you cannot fill two trees. This is because the level cap is 60, giving you 51 talent points. This usually makes it hard to choose what you want to do (at least it should, if the class is well balanced.)
IGN has a recent and very well made talent planner for each class. Play around with it and see how it works.