You can gain one Hourglass for every guest you manage to invite to the party. The catch is, you have to answer all three of their email questions accurately in order to claim them.

How do you get an hourglasses on the first day?

Hourglasses appear randomly whenever someone's chat bubble has cute emotes around it (like the cloud outlined ones or the hearts that surround them – I believe there is a higher chance of gaining them when you select a favourable answer for the characters).

How many hourglasses do you get from Zen's route?

See V / Route Tips for hints on how to reach both ends. The story consists of six episodes, with two separate closing episodes that each require 80 hourglasses to unlock and remain unlocked forever after purchase.