Quests for Classic dungeons come from outdoor quest lines, typically in the zones where the dungeons are located. In certain later dungeons you'll find quests inside, but that practice did not really start in earnest before the LFG system was created. This means that in case you would like to do dungeons while leveling, you will often finish a zone first, then try to discover a group for this zone's dungeon.
If you are brand new to, or leaping right into, the World of Warcraft encounter, we hope this WoW Classic starter guide has been convenient. Don't forget to have a look at our other guides for more-specific tips on World of Warcraft Classic.