How to transfer WordPress site?

I have set up a WordPress site (themes, posts, pages, images in Media Gallery etc). I now have to transfer the entire site (content and everything), to another web server. The other hosting company has set up a WordPress site in my account, so I can transfer what I have done in another web server to theirs.

Can I do it through FTP?

I am new in this, so I don’t know what file I need to transfer and how I should do it. The only thing I know is to upload the theme I am using to the new server. But what about the posts and pages and images etc.

Please help … thanks!