Most of the Boost libraries are header-only, meaning that there's nothing you have to compile or link to.
Make sure you are getting the most recent version of Boost:
Header-only libraries can then be used by simply including the respective header files.
A few Boost libraries require compilation:
Also, the following libraries have components which must be compiled:
The source for Boost can be obtained through the download link on the site, which will re-direct to its SourceForge page for the latest version (1.61.0 as of July 2016). This can be unzipped (or un-tared, etc) to a directory (such as C:\local\boost_1_61_0). This directory can then be added to the include path for the software you are building. After this, you can include Boost headers in C++ files with
The majority of the libraries in Boost are header-only. If you only need these then the above source distribution is all that is needed. However, if you need to use one of the libraries that requires a compiled binary to be built, you will need that as well.
On Windows with Visual Studio, an alternative to building the libraries yourself is to download pre-built libraries from Boost's SourceForge page (1.61.0 as of July 2016). On that page you can select an installer that will install a version for a specific Visual Studio build or the 7-zip file (boost_X_XX_X-bin-all-32-64.7z) that contains the binaries for all the supported Visual Studio versions. Either of these options includes the source/headers as well as the binaries, so there is no need to have downloaded the source distribution above. Once you have it, extract/install to a directory (such as C:\local\boost_1_61_0) and add that directory to your include path, then add the directory containing the binaries that correspond to your version of Visual Studio (e.g. C:\local\boost_1_61_0\lib32-msvc-12.0 for Visual Studio 2013 32-bit projects) to the library path.