External hard drive folders not viewable from Macbook air

I have a mid 2009 Macbook air, and recently purchased a 1TB Seegate external hard drive. I reformatted the drive for Mac and backed up my files but cannot see the folders, to confirm that all my pics are there. I am a new Mac owner and don't know a lot about how to navigate the drives. On Windows I used Windows Explorer to see the folders but on my Macbook air, I have not found an equivalent tool to see the folders and pics.
(I am a Canadian visiting Spain and taking pics daily and my Mac hard drive is full and won't let me download any more pics, and my camera disk is almost most full. I can buy a new memory disk for the camera, but I just spent $140 on the external hard drive to avoid this.)
Thanks for any help you can offer.

Did you see the icon of the external hd on the desktop ?
If not Finder > Preference> General >check HD option
Put you're mouse pointer on external hd icon click on wright of the mouse and than option open

finder should show you the external drive.
the easiest way is to load your photos to macbook air and using Carbon copy clone to external drive, this way you have the photos on your external drive,

Finder is the OSX 'equivalent' of Windows Explorer.

You should see you external hard disk in the grey sidebar down the left of Finder.

If you can't see the sidebar go to the View Menu - Show Sidebar.

The disk should show under 'Shared'.