Well, it’s not just Thom; Jonny is responsible for A LOT in terms of beats, and Ed and Colin and Phil all actively participate as well. For example, 15 Step was done on Jonny’s Analogue Systems setup, but it was Jonny and Ed working together. Jonny also created the beats for songs like Idioteque and The Gloaming.
Thom’s own methods can probably be split into two categories: computer manipulation and drum machines, and of course the two get mixed quite a lot and sent between eachother I’d imagine.
For his drums machines, see this section of his page. The one that he’s been using quite a lot since at least In Rainbows is the Elektron MachineDrum SPS-1 UW. The Machinedrum is extremely powerful, so I’d imagine that at least some of what used to be done on computers is now done on it.
For software(mainly cutting up stuff etc), he uses Digidesign Pro Tools a lot, although you should also look at this section of Nigel’s page, since Thom and Nigel work closely on computer work.