I ran into a couple of questions while playing D&D 5th:
- Does drawing a weapon take an action?
- Does picking up a weapon from the ground take an action?
No, drawing a weapon does not take an action. Nor does picking up a dropped weapon. Both answers are found in a sidebar on page 70.
Note that you are allowed to interact with only one object per turn for free (p. 70, Other Activities on Your Turn). You can draw or sheathe a weapon, for free, but to do both in same turn you need to take the Use an Object action (p. 72).
You can draw, or pickup a weapon without using an action, but only one of them.
In the Player's Handbook there is a feat called Dual Wielding. One of the benefits of this feat is the ability to handle two weapons for free during your turn, rather than just one. Player's handbook page 165
This makes it clear that the initial rules about only interacting with one object as a free action is not only RAW but also RAI. So you can draw, or pickup a weapon, but only once. If you want to interact with a second object, you will need the "Use and Object Action" unless you have the Dual Wielding feat, in which case you can draw or stow two weapons.