Players get, depending on the class they have chosen, lots of spells and skills. The higher they go in tier, the more spells and skills they get.

Spells and skills get practiced at the hundreds of Trainers that are spread across the Realms at a certain price.

A few basic skills and spells can be practiced at a Guildmaster, to get you on the way. Each clan has his own guildmaster and there is also a guildmaster north east from recall.

The Trainers and Guildmasters can be recognised by the cyan [T] in front of their name. When you're in a room with a Trainer, type practice skills to see what skills the mob can teach you, or practice spells for the spells. If you type these commands in a room without a trainer, you'll just see the list of skills or spells you currently can train.

Notice that in some cases you need to train one skill/spell before another one will work, (so called pre-requisite skills).

Of course spells and skills can also be maxed by using them but you still have to train them at least once at a Trainer.

To see the available spells at your level: type practice spells.
To see the available skills at your level: type practice skills.
To practice an actual spell or skill: type practice < spell/skill >
To see a list of all the skills and spells a certain class will get type: skilllist < class >

Once you have reached the maximum (97%) in a skill or spell, the player will also receive a bonus of experience points. This bonus is 20% of the experience you still need to reach the next level.

Next to the helpfiles, you can also find more information about a certain skills or spell in-game by typing spellinfo skill/spell.

List of all the Skills.
List of all the Spells.
List of the Trainers per Dimension.

For info about which Skills/Spells each Class gets, see the sublinks under the Page Classes