How to install a latex package in MacOS TeXLive?

if you have mactex 2009 or later (and why wouldn't you?!@?!) then use tlmgr from the command line to update and add packages:

tlmgr install packagename

and to update: tlmgr update --self then: tlmgr update --all

You should extract the package into ~/texmf/tex/latex/$PACKAGENAME and run latex from that folder. After that you should run texhash or mktexlsr from your home folder

Instead of manually installing packages you could to install the package bundle which is suitable for your operating system. In your case you could install the bundle texlive-lang-cyrillic which contains the cyrillic package as well as needed fonts such as the LH fonts. You can read about the contents of macport packages here:

https://trac.macports.org/wiki/TeXLivePackages

Thus, you may execute at the command prompt:

sudo port install texlive-lang-cyrillic

as mentioned in Using port install.