Artists, how do drawing tablets work?

It really depends on what kind of tablet you are asking about.

An iPad or similar, touch-screen tablet computer.

Or a Wacom or similar tablet.

The iPad-type has its own screen and is a solo computer it does not need any additional parts and you draw on the screen using a stylus or your finger, there are any number of drawing softwares (apps) available many of them free and several are very good.

The Wacom-type is essentially the same as a mouse, it is connected to a standard desktop or laptop computer and operates the software already on your computer (the tablet might come with a package of software too). So you could use the tablet to navigate a spreadsheet as well as to create a drawing.

Both are viable ways of creating digital drawings, they each have pros and cons.

Think of a drawing tablet as a computer monitor and a computer mouse in one. The difference is that the mouse is replaced by a digital pencil and you're actually drawing on the screen itself. Because tablets are computer hardware, they are used to interact with other software programs such as Photoshop, which are drawing and photo-manipulation software. So for example, you open Photoshop on your computer, with the drawing tablet connected to your computer and turned on. You will see the Photoshop composition screen and tools on your tablet screen and there you can use the digital pen to draw on the tablet inside the Photoshop (or other) program. This is a basic explanation, but I hope it helps.

Usually the come with software, but it will be a basic program. If you want something more elaborate then you will have to buy it yourself.

It's like drawing on a piece of paper, with a pen or pencil. Some software is usually included and some must be purchased, like always. The free stuff isn't Photoshop....