Copy your entire iPhoto Library as a unit from the Pictures folder in your Home folder onto the external drive — just drag the iPhoto Library onto the external drive's icon or into its open main window. Do NOT try to copy your photos any other way than this.
After the copy is finished (it may take a while if your library is large), open iPhoto while holding down the Option key, and select the library on the external drive for iphoto to open. If it opens normally and everything seems to be in order, you can delete the iPhoto Library file from your internal drive. Don't forget to empty the trash afterward.
REMEMBER THIS: Now that your iphoto Library exists only on the external drive, it is not backed up! Back it up on a second external hard drive, or sooner or later you will lose it to a hard drive failure. The one sure thing about hard drives, like all other mechanical devices, is that eventually every hard drive will fail. Don't wait for it to happen and then think about the backups you should have been making all along!