They work the same way as internal drives. Generally they are connected via USB, so access is slower. If you have USB3 then access will be faster than it would be with either USB1 or USB2. But still slower than an internal drive. You can also connect an external network drive, which will be much faster than a USB drive, but still not as fast as an internal drive.
In general once connected the external drive will show up as a device in you file system. On Windows it should be automatically mounted and assigned a letter identifier, such as D: E: etc.
Then you just have to check whether it already has a file system on it (i.e. folders and file structure). If it does not right click on the drive ID (e.g. D:) and select the format option, which will create a file system on the device.
On Linux, the device will show up in the /dev directory with a name something like /dev/sda or /dev/sdb, etc. The "sd" stands for SCSI device, and it is sort of a legacy designation for drives. Then you need to run a utility to format the disk, and configure the disk partitions to be mounted in the Linux file system.