To upload files, you just use a simple FTP rogram. You can choose what you like. WinSCP, FlashFXP, WS_FTP, Dreamweaver, EditPlus, CuteFTP, 3-D FTP, the list goes on and on. Choose one you like, use it.
Since it's a *nix server (most likely) you'll be connecting to your folder already. So what you need to do is just upload to the directory named: public_html or www. Either will work. Since you say it's a webserver, you only need to upload the php files you'll be working with. If you're using a CMS (Content Management System) or Forum Software, you'll need to follow their instructions.
As for the database setup, localhost is environment dependant. So localhost for you will be your computer. When you upload it, it will be the webserver. If you do change it, you'd be better off changing it to an IP address rather than domain. You just need to make sure that the database is created on the webserver as you have it set up on your computer.
Hope that makes sense.
~Brett
