Start by downloading blackberry desktop software for Mac here http://us.blackberry.com/apps-software/desktop/desktop_mac.jsp
Complete the following steps to back up BlackBerry smartphone data:
Note: To perform this task on your BlackBerry smartphone, mass storage mode must be turned on.
Note: If you encrypted the data that was backed up, type a password when you are prompted.
This is information from the blackberry website on specific steps to back the phone up to a mac computer (http://www.blackberry.com/btsc/search.do?cmd=displayKC&docType=kc&externalId=KB18776). Hope this helps.
Check out a fun infographic that teaches you how to increase storage, enhance security, improve battery life and clean your device.