Can one presume that this external drive is being shared with a Windows machine?
If so, and you were late to the dance, the drive may be formatted as NTFS which the Mac can read but cannot write to.
Couple of ways around that, one free and one not so free.
NTFS for Mac by Paragon is a very good piece of software that enables your Mac to read and write to an NTFS drive. This one is not free. Find it at http://www.Paragon-software.com.
NTFS-3G also does the same thing but is a little more difficult to install. It is Free.
Find it at http://download.cnet.com/NTFS-3G/3000-2094_4-10913782.html
If the drive is not formatted as NTFS, get back with us
I have an external hard drive that is connected and is being recognized but it's not shared (I can only read). Is there a way to share it out?