This sounds easy and I thought Sharepoint was supposed to be web development for dummies.

I am trying  to make a simple time card for my employees. I want to be able to connect two list so that when a user chooses something from the first dropdown it will affect their choices in the next dropdown.

For example, if a user chooses Flash from the Department dropdown i want the choices in the next dropdown called Tasks to only include the tasks related to the Flash team.

Honestly, this kind of feature is not just branching lists. It involves lookup, filter and so on. So it is a complicated process.

I recommend you take a look at SharePoint Cascaded Lookup, which is exactely what you are after. Maybe it brings some hints to you.