Head to the Boost homepage here. Under "Downloads", "Current Release", click the download link. This will take you to a list of different files. These are the same directory, compressed in different ways. Select one that you will be able to open (e.g., the .zip file). This file is large, and may take some time to download. Once the download has completed, extract the compressed directory to the location that you would like to install boost.
Next, open a console (if you are in Windows, this is the "Command Prompt" app). Navigate to the extracted directory. Type into the console "bootstrap". This should generate some text saying "To build, run:". Run this command (e.g., "./b2"). This should result in several more pages of text, ending with two important paths: the include path and the linker library paths. Ensure that you have set up your include path and linker library paths to include these directories and you are done!