You'll either need to install Flash from the Adobe website just like you did on your PC, or install Google Chrome, which has Flash built-in.
Your difficulty my reside in the security settings of your Mac. Open SYSTEM PREFERENCES, select SECURITY & PRIVACY, and check under the GENERAL tab that ALLOW APPS DOWNLOADED FROM: is set to "Mac App Store and identified developers." Then go to http://get.adobe.com/flashplayer/, and click the INSTALL NOW button. A .DMG file will be downloaded to your DOWNLOADS folder. Single-click the .DMG file. The double-click INSTALL ADOBE FLASH PLAYER. If you get a permissions error, then you may need to change the ALLOW APPS for "Anywhere".