All of the members of Radiohead have used a variety of different processes to write different songs. It really just depends on the track. Some songs (most, to be honest) are written by Thom on a guitar or piano along with vocals and lyrics. Sometimes, he would then play it for the rest of the band, who would play along and come up with their own parts. Eventually the original guitar or piano part might be discarded, new sections added, and it evolves into something totally new. For some other songs, Thom would sketch them on some sort of rhythm box, like his old Boss Doctor Rhythm Drum Machine and especially the Yamaha QY70 (the original demo of There, There is a good example of the Yamaha). Sometimes songs, such as And It Rained All Night and Honey Pot, are remixes of other songs (The Gloaming and All I Need in those cases) which then turned into songs of their own, or from parts of old songs which are reused (like the beat of the old version of Killer Cars being used for Planet Telex). Some grow from a short samples of demos by another member of the band (The Eraser), or from heavy modifications of recordings of another member (Treefingers). Other songs, such as Idioteque and 15 Step, are born largely out of beats and/or samples (and/or beats made out of samples), rather than a premeditated chord structure or riff, many of which (such as Idioteque) aren’t even written by Thom. Some tracks, like Dollars and Cents, were originally recorded “live jams” (live meaning the whole band playing together, not meaning live performance) which were then cut up and shorted to work as a song. Some tracks are deliberately styled after other artists, such as Subterranean Homesick Alien (inspired Miles Davis’ Bitches Brew). Some songs are written in a hotel bathroom on tour, some are written at a band member’s home, and others are written in studio.
In short, there are about as many songwriting techniques used as there are songs. Radiohead don’t follow any sort of premeditated formula - they work forward from whatever inspiration they have!