By default extensions in stable states can be installed through the Magento Connect Manager tool.

If you want to install an extension which is in alpha or beta state you need to get the extension key. Then you should open your Magento admin area->System->Magento Connect-> Magento Connect Manager. You will be prompted to enter once again the admin login credentials.

Log in and navigate to Settings. In the Preferred State drop-down menu you can switch between the Stable, Alpha and Beta states. Once you are ready, save the settings and return to the Extensions area. There you can paste the extension key and install the extension.