You can do a Get Info on the drive, and set the permissions you want and then click on the button next to the '-' and select apply to all enclosed items. You may need to login as root to be able to do this.
An alternative, and this carries a big warning,is to go through the Terminal. cd to the top level of the disk which is usually /Volumes/<volume name> and type the following :
chmod -R 777 * followed by Return and enter your admin password when prompted.
I must stress that you must make sure you are at the TOP LEVEL of the Volume or folder whose permissions you want to change as this will give read/write and execute permissions to everyone on that folder and all sub-folders and files.