1. Download Magento from http://www.magentocommerce.com/download [ Make sure, you are downloading the latest Stable Release].

2. Make a database at your WAMP server’s phpmyadmin interface.

3. After you have downloaded the Stable pack’s zip package, extract it to your PC’s local folder and move the whole magento folder into your /wamp/www/ . So,it should be accesible at http://localhost/magento/

4. Now enter http://localhost/magento/ on your browser and it will come up with a browser installation Step-by-Step Wizard.  Just proceed with it and make sure, you dont make any changes in that wizard options, if you are not sure, what you are doing.

5. The second step, where you enter the database details, will take a while, since that step stores the tables in the database. So, hold your fingers, till it shows the next step on your screen.

6. Now, the next step will ask you to enter the admin details and you are done.

7. Test your new Magento store at your browser then.

If you want to install Sample Data in your test store , then check this article.

Installing Magento on localhost, has a bug of not letting the admin to be logged onto the admin panel. So, if you want a fix to it, then check this article.