There is an Action Bar at bottom of the User interface. Each class starts with some skills. Every few levels, you will unlock new skills specific to your character class, these can be learned from your Class trainer. You will be introduced to one of these NPCs during one of the first few quests you complete in your starting zone, but they can also be found in many towns and each of your Faction's cities.
World of Warcraft Classic is currently in beta, which means some players are getting a chance to experience a much older version of the MMO ahead of its release. WoW Classic is based on how WoW played in August 2006, back around update 1.12. Back then, things were different. Tauren hitboxes were much larger, sitting could cause certain combat effects to not trigger and completed quests were marked with dots and not question marks. Strange days.