Ensure that you are logged in as an administrator on the machine which you would like to install Steam on.
If you have previously installed Steam and are reinstalling to remedy a problem with your prior installation, please see the Uninstalling Steam topic for instructions to remove any prior Steam installations.
Also please check the Troubleshooting Network Connectivity topic to ensure the required ports for Steam are open on your network.
Download and run the Steam Installer from steampowered.com.
Source of the information and additional details can be found here.
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