I have been playing D&D 5e for a while now and I recently made a new Fighter with 2 weapons. I already read many things and the PHB but I can't figure out if I get a bonus action from my first attack so I can make a second attack or if I have to already have a bonus action. If so wouldn't it be really bad on a fighter, at least in the early game? And how do I get this Dual wielding thing so that I get to wield normal weight weapons?
But you can take only one bonus action, and only on your turn.
See Basic Rules, Bonus Actions:
You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. You otherwise don't have a bonus action to take.
You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available.
Attacking with a Light weapon explicitly allows you to take such an action.
See Player's Handbook, Two-Weapon Fighting:
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand
For more info see Two-Weapon Fighting & Bonus Actions