The exact requirements will depend on many factors, your estimated board traffic being one.

You must have a webserver that has PHP 4.3.0 (or better) and MySQL 3.23 (or better) installed. If you are unsure whether your server has these programs installed, please check with your web host now. If you are capable, you can always download PHP and download mySQL and install it yourself. If your web host does not support PHP or mySQL, consider hosting your entire web site or forums with IPS Hosting services.
Invision Power Board works best on an Apache server, and is Apache 1 and Apache 2 savvy.

General Requirements
You do not need a new mySQL database as Invision Power Board supports table prefixes to prevent tables being overwritten.
You will also need the mySQL username and mySQL password for a mySQL user that has permission to "CREATE", "DROP" and "ALTER" tables.
You will need about 5mb of free web space and roughly 5mb of mySQL database space to allow installation and a moderately sized community.
If you are unsure on any of these points, please ask your webhost before proceeding.