The iPhoto library is easy to backup, because it appears as a single file (its a package, in other words).
The library is stored within the Picture folder of your home folder. The full path is:
Macintosh HD >> Users >> Yourname >> Pictures
There you can find your “iPhoto Library” icon, that can be quite heavy (several gigabases). Just drag and drop this icon to an external drive to copy it. Because of its size you should remember that FAT32 formatted drivers support files up to 4 Gb, so you should choose a Mac formatted drive (or at least NTFS, provided you have the appropriate driver.
Hint: if you want to browse the library as it would be a normal folder, right click on it and then click on “Show package content“.