The Zelda games are very linear, you follow a story line from the beginning to the end exactly how the game is made to be followed. Then the game is over.
In Elder Scrolls games, you can go off and do whatever you want to do. Bring up the journal (start menu if you're on a console) and look at what quests you have in it and see if you want to do any of them, or just don't and travel, explore, and find things you want to do. The whole deal with the dragons is the Main Quest, which is the line of quests that is the staple of the game. Maybe you want to do that first to get into the game, and if that's the case then right now you should have the "Talk to Jarl Balgruf in Whiterun" (or something) objective in your journal, and if you activate it you will get a marker on your map which tells you where to go.
For example, I'm 85 hours in, and I've:
Completed about 15 or so side quests out of the hundreds that are in the game.
Been to less than half of all the dungeons and locations.
Progressed a bit in four of the seven main quest lines.
Not completed a single quest line.
Completed about 60 miscellaneous tasks out of literally an infinite amount.
What have I done in 85 hours then? Explored, taken in everything, done some quests, progressed in skills. You can play this game and complete every quest in 10 hours if you like. But that's not playing an Elder Scrolls game.