To run WordPress on a local machine you will need something like WAMP or MAMP (Windows, Apache, MySQL and PHP or Mac, Apache, MySQL and PHP). Basically you will need to run a server instance on your local machine – WAMP and MAMP provide stand-alone setups that are pretty user friendly.
Once you have WAMP/MAMP installed, launch it. Then using PHPMyAdmin, create a new MySQL database for your WordPress site. Download and unzip WordPress into the htdocs folder for your WAMP/MAMP installation.
Please be aware that sites running under WAMP/MAMP are not accessible via the internet. This is for security reasons. While you can work around this and make the site accessible over the internet, it is better practice (and safer) to put it on a properly configured and secured server.