My friends and I are really new to D&D, and we couldn't find a good answer in the Starter Set rule book. We've been treating taking out a weapon as its own separate action, but would switching weapons entirely count as a full turn?
You get one free item interaction per turn, which includes drawing a weapon.
Player's Handbook (PH) page 190 (or the free Player's Basic Rules, page 70; Starter Set Basic Rules, page 9):
You can also interact with one object or feature of the environment for free, during either your move or your action. For example, you could open a door during your move as you stride toward a foe, or you could draw your weapon as part of the same action you use to attack.
If you want to interact with a second object, you need to use your action. Some magic items and other special objects always require an action to use, as stated in their descriptions.
And the use an object action, PH page 193 (PBR page 72; Starter Set Basic Rules, page 11), states that "This action is also useful when you want to interact with more than one object on your turn."
As for switching weapons, you get one free item interaction per turn. Meaning that on your first turn you can draw a weapon for free. On Turn two you can stow a weapon (for free) and use your action to draw a second weapon. Unfortunately, this means that you don't have your action to attack with it, but you can use it for opportunity attacks.
That being said, as @Dale M pointed out, you may drop a weapon for free, leaving you with your free item interaction.