The drive's formatting can be seen in the information window as well as in Disk Utility, and clicking the check box at the bottom of the window will ensure the drive's permissions are ignored. Unfortunately even though there are third-party drivers and workarounds to allow OS X to write to NTFS drives, these features are not supported by default, so such drives will only be mounted read-only. Often commercially available drives will be formatted to FAT32 and therefore be fully compatible with both Windows and OS X however, many popular drives (especially high-capacity ones) may be formatted to NTFS by default.
The first detail to check is if the drive is formatted to the popular NTFS format used in Windows systems. Do you have an external hard drive that you cannot write to on your Mac? While most external storage media's default formatting and other setups should make them both readable and writable on most Mac systems, there may be times when this is not the case.
