Drawing tablets are mostly quite well supported on Linux, since at their most basic they are essentially touch activated mouses.
Most drawing tablets, however, are much more than just a pen-shaped mouse; they have pressure sensitivity and programmable buttons. Whether these features are supported or not depends on the manufacturer of the tablet.
Wacom, the most ubiquitous tablet vendor, employs a programmer for Linux drivers, and has had impeccable support for Linux for years. If you want guaranteed tablet support, buy Wacom.
Plug a Wacom tablet into your computer and check to make sure the Wacom driver has loaded by listing the active modules:
$ lsmod | grep -i wacom
Wacom tablets, like most tablets, are plug-and-play for basic use. To configure the advanced features (the ones you probably bought the tablet for), you need to install a Wacom settings extension from http://slackbuilds.org/result/?search=wacomtablet&sv=
Find the Wacom configuration panel in System Settings.