Download QGIS from http://www.qgis.org/ .
For Windows, choose the option “independent installer”, 32 or 64 bits depending on your machine. This should be the only program you need to install.
For Mac OS X, you will be redirected to another site (KyngChaos.com) where you will need to install some required packages (GDAL and GSL) before installing the QGIS package. Be sure to download and install each of the necessary packages (and optional software for GRASS and Python if you wish) before installing QGIS.
As with all open source software, the best helpers can be found on the mailing lists and online forums associated with the software. If you have consulted the documentation online and you can not solve a problem, do not hesitate to ask your question on the mailing lists. More experienced users are generally happy to help you.
The QGIS mailing list:
After installing QGIS, try to start it. You should get an empty window with a toolbar at the top. Now, we’ll have to add some data!