I have a maxtor USB external hard drive, from the 'my computer' icon, if a hd is connected, it will show up just like any internal hd, allowing you to browse its content or copy/cut files over. on a modern version of windows, xp and up, windows should detect your hard drive and use its own generic drivers to allow it to work. the disc you receive with your external hd may have various data related backup and safety tools for you to use or try out, along with their own drivers.
There are differing connection types for external hds with different data transfer rates, but external hard drives still work at a slower speed than internal. installing and running software from one is possible, and writing a cd or dvd is too, but high capacity drives are generally intended for backup-writing at a slower speed from an external is recommended in comparison to internal for a successful burn-but for either type of hd, the slowest write speed is always recommended