1. First you need to get the QGIS software online, or at the QGIS homepage, click on the "Download Now" button. QGIS is available for a lot of operating systems, it runs on Linux, Unix, Mac OSX, Windows and Android, and supports numerous vector, raster, and database formats and functionalities.
2. Depending on your operating system, follow the instructions and download the appropriate installation files for QGIS.
If Applicable: A prompt may appear preventing files to download, if this happens, keep the files for download to disable the warning.
3. Once the download begins, you may accept all the default settings for quick use. It is not necessary to download the demonstration data, but this option is available during installation. When the installation finishes you will have new programs installed ready for use.
4. QGIS is an official project of the Open Source Geospatial Foundation (OSGeo) and is completely free to use, but to support it you are encouraged to help by getting involved and/or by donating in any way you are able. This includes, though not limited to: reporting bugs, participating in support channels, helping with translations, or developing plug-ins.
Learning QGIS - Third Edition by 
Mastering Qgis
Open Source GIS by 
QGIS and Generic Tools by 