According to a help article, Square is described as a "the easiest way to send money to anyone, using just email and your debit card."
Unfortunately, at this time the service is invite only. Meaning you will need to wait for an invitation to be sent to you from the company before you can use it.
A Square representative told TechCrunch, “We’re excited to share Square Cash with our friends. We’ll continue to invite others to try it out in the coming weeks.”
You can check out the splash page at the link below. Notably, Google recently announced that it's updated Gmail to let you attach money to emails via your Google Wallet account.