Why does a plastic ruler that has been rubbed with a cloth have the ability to pick up small pieces of paper? Why is this difficult to do on a humid day?

The same charge repels and the opposite charge attracts.

During rubbing, a static electric charge generates in the ruler.

When the plastic ruler is rubbed with a cloth, a static charge is developed in the plastic ruler. Now when the ruler is close to some small piece of paper, they polarize the small piece of paper. Now the piece of paper is attracted by the ruler due to electrostatic force. As the weight of the small piece of paper is less than the electrostatic force due to the plastic ruler, they move to the ruler.

On a humid day, the quantity of the water molecules in the atmosphere is greater than the normal day, and the water molecules are polar due to which the charge distribution is divided in between the ruler and the water molecules, due to this, the pieces of paper are less polarized and attracted to the ruler.