Moving to my own host

So, I’m wanting to move to my own host, I currently have a wordpress.com hosted blog and want to branch out, but I have a few questions. For example:

When I buy my hosting site, does that mean the blog is immediately transferred over there (I already own the domain name), or do I need to do the full install etc before the blog is hosted there.

I’m planning on getting dreamhost so I dont know if that matters or not

thanks!