If you're a newcomer to the Mac OS, see these:
Switching from Windows to Mac OS X,
Basic Tutorials on using a Mac,
Mac 101: Mac Essentials,
Mac OS X keyboard shortcuts,
Anatomy of a Mac,
Switching to Mac Superguide, and
Switching to the Mac: The Missing Manual, Lion Edition.
Additionally, *Texas Mac Man* recommends:
Right click on the external hard drive icon and select Get Info, a new window will open.
At the bottom of the new window, there is a Permissions section. Next to your user name there is an option with arrows. Click this and select Read & Write. This gives you permission to access the external drive to either write files to or delete files from the external drive.
If it already says Read & Write next to your user name, it could be the drive is formatted in FAT 32 or NTFS and the video file is too big to be copied over (FAT 32) or the NTFS file system isn't understood in Mac OS X. You would then have to use Disk Utility (Applications> Utilities> Disk Utility) to reformat the drive to GUID (in options) and Mac OS X (Extended). You can name your Hard Drive in the Space above Mac OS X (Extended).
Hope this helps
Is this a drive that was used with a PC? If so, it will likely be formatted NTFS which Macs can only read, not write to, without special software. If you are now only going to use it with a Mac, consider formatting it for Mac use. if it must be left PC-capable we can recommend software for that (either for making Macs work with PC drives, or PCs work with Mac drives).