Hydrostatic pressure

There are a couple places where pressure is pushing against the card. First the atmospheric pressure or the tiny air molecules all around us are randomly colliding with the bottom of the note card. This pressure holds the card up, but why doesn't the weight of the water push the note card down? Isn't the weight of the water enough to overcome the atmospheric pressure pushing against the card? That's what most people would think, but if you look at the top of the glass of water (formerly the bottom), you'll notice a small pocket of air. Actually there isn't much of an opportunity for air to get into that space, so what we've created is a small pocket of low pressure. There are more air molecules pushing up against the bottom of the note card, creating a higher pressure area compared with the lower pressure area inside the air pocket in the glass. The force from the atmospheric pressure holds the card up and the low pressure zone in the glass prevents the water's weight from pushing the card down.

Adhesion occurs because water molecules, having the positive and negative ends, are also attracted to other materials. In the experiment, the water molecules are attracted to the paper, adhering to it, while continuing to keep the surface tension with the other water molecules. This keeps the note card in place.