How and where can I deploy my database in the clouds

I built a ruby application, and now I have several doubts to implement it.

How and where can I deploy my database in the clouds? can be for mysql, postgresql, etc ...

which web server can I use, and do I need an application server?

I'm kind of confused about the implementation, this is my first project, and just a simple personal project for learn how web applications work. I've seen a bit about Heroku, but I'd like to know how I can do it separately (database hosted on clouds)

Thank you very much