The first question you should ask is whether the package you are trying to install is already installed on your system. If you are using MacTeX as your distribution (which you probably are) then most packages are already available. Within TeXShop you can choose the "Show Help for Package" item from the Help menu and enter your package name. (Or make a simple document that loads the package to see if it doesn't exist.)
If the package doesn't exist, then this answer: How to have local package override default package covers everything you need to know.
On a Mac, local additions go into the Library/texmf folder of your Home folder. (~/Library/texmf) You never need to update the file database for local additions to this folder. If the folder doesn't exist, you will need to create it yourself. For a one-click version of this you can use this utility: Make Local texmf Folder (Disclaimer: I am the author of this).
Note for OS 10.7 or 10.8 (Lion/Mountain Lion)
If you are running OS 10.7 (Lion) or later, your user Library is unfortunately a hidden folder. It is, however, easy to access it through the Finder's Go menu: hold down the Option key while choosing the Go menu, and the local Library folder will appear in the list. Alternatively if you type Command-Shift-G you can enter the folder path directly (~/Library/texmf)
