The minimum (and maximum) you need to run WordPress is a web server (Apache, IIS, a couple of others), PHP (the scripting language in which WordPress is written) and MySQL (the backend database).
If you’re intending to run it on a local machine, there are prepackaged installations available for both Windows and Linux (see WAMP and use your Lixux flavor’s package manager, if using Linux, to download LAMP) that make setting up the environment relatively painless.
Once installed, download the WordPress package from this site, uncompress it into a directory, and follow the install instructions.
You may have something of a learning curve involved, but it’s probably best if you ask specific questions where you experience problems, rather than anyone attempting to address everything you might possibly need or want to know about all parts of that environment.
If, by the way, you’re looking to host it on a remote web server, there are many that offer Apache / PHP / MySQL services, and quite a number that have automatic or requestable install utilities for WordPress.
