Contrary to the modern game, there's absolutely not any official'looking for group' system that finds people to play with you and TBC Classic Gold teleports all of you to the dungeon. Instead, you're look for party members in conversation channels in major cities or on your guild, and you may all fly or run together to the dungeon you wish to do. And you will have to go there -- in the first days of Classic, there will be no summoning stones at the instances themselves.
Quests for Classic dungeons come from outside exploration lines, typically in the zones in which the dungeons are located. In some later dungeons you'll find quests indoors, but that practice did not really start in earnest until the cheap WOW Classic Burning Crusade Gold LFG system was made. This means that in case you would like to do dungeons while leveling, you'll often complete a zone , then attempt to discover a group for this zone's dungeon.