To sync your account, you'll need to allow "less safe apps" to connect to your gmail, or something like that. You can change that
here (just scroll down all the way and enable it)
Now that you've dealt with that, you have to send a message with anything wrote on it, and put a hyperlink with the vita file path (the "email:send?attach=ur0:shell/db/app.db.", without quotes) on the message you wrote. Send it to yourself.
Open the email app on Vita and check the email you've just sent to yourself. Click on the message with the hyperlink and it will redirect you to a new email with the file attached. Again, send this email with the attachment to yourself.
Go to your PC, open the email and download the attachment.
As many said here, for now this procedure is just a "hey look, we can dump system files, check it out!11", so the file attached you'll get won't be of much use - you can download a SQL software like DB Browser for SQLite to take a look at the file, but that's it. We don't know yet what this exploit is capable of (until tomorrow, that is.)