That drawing style's typically known as 'cell-shading'. For such smooth lineart, I'd imagine the entire process is done digitally on programs such as Photoshop or SAI. It's a style I've used myself! People sometimes do the linework traditionally (pen and paper), but it's often much faster and easier to work from scratch in photoshop.
While I'm not certain about hand-held tablets (I've only ever used a good, old fashioned PC for art), a laptop should certainly be able to run a good paint application!
A quick dA search also brought up loads of tutorials. You could likely draw in a similar style with ink and markers on paper, too-- though these are admittedly extremely expensive!
Hope that made sense. It's one of the easier styles to learn!
