I check Public Tableau and there seem to be no obvious documentation yet.
For clarity, please mention the guidelines and rewards if any for Viz of the Week and Viz of the Day.
You're able to submit your own visualisations to the Tableau Public team if you believe it is worthy of recognition, or another Tableau Public visualisation which you think deserves to be! The criteria for it is very open, but I believe they look for something current, interesting and/or beautiful.
But really, there's no real criteria - the objective of Tableau Public is to share, showcase and use it as a learning and development platform - this is one of the best things about it!
what do you mean with the submission? Just uploading a workbook by tableau public?
Yes, uploading to Tableau Public, but also tweeting the Tableau Public team as well (@tableaupublic on Twitter) - Also check out this post by Ryan Sleeper on how to signal boost your vizzes: https://public.tableau.com/s/blog/2016/03/5-tips-making-your-tableau-public-viz-go-viral
Let me know if this helps!