For example, does the Cunning Action allow a 5th level Rogue to have a bonus action, thus letting him fight with two shortswords? I don't think he would have any other bonus action unless wielding two light weapons allowed him to attack with both. Thanks for the help.
For the Rogue Cunning Action, PHB pg.96:
Starting at 2nd level, your quick thinking and agility allow you to move and act quickly. You can take a bonus action on each of your turns in combat. This action can be used only to take the Dash, Disengage, or Hide action.
When Dual Wielding, PHB pg. 195:
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. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative. If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.
What this all boils down to, is that you have one action, one movement, one bonus action and one reaction per round. If you use your cunning action, that will burn the bonus action for your turn, and you will be unable to utilize your offhand weapon. At any time you can dual wield weapons. If you are using the feat rules and you have Dual Wielding, you can dual wield any one handed weapon instead of just light weapons.
A bonus action is not something you 'get' from having Cunning Action. You always have a (note the singular) bonus action, Cunning Action just gives you more options to use it on.
The dual wielding rules themselves already allow you to use a bonus action to attack with your off-hand weapon; dual wielding has nothing related to Cunning Action.