How much does a star actually move when a planet pulls on it? I went and looked it up again, because I'd misremembered the number. About 50 metres a second — motorway speed, roughly — toward us, then away, then toward us again. That's it. That's the whole thing.
Mayor and Queloz never saw 51 Pegasi b. They watched the star's light go faintly blue, then faintly red, on a four-day cycle, and worked backwards from the rocking to a planet about Jupiter's mass sitting ridiculously close in, which in 1995 nobody was expecting and plenty of people wanted to check twice before believing. The star's roughly 50 light-years off. Pegasus is high in the southeast after dark — the big empty square. It's in there.
It's the ambulance effect, basically — pitch rises as it comes at you, drops as it goes. Only here you're reading it off the dark lines in the star's spectrum, which shift a hair blue then a hair red. Mayor and Queloz had to build a spectrograph steady enough to see 50 m/s against all the noise. Lovely instrument work.
The bit that made 50 m/s readable was unglamorous plumbing: ELODIE took the starlight down an optical fibre to a spectrograph sitting still in its own room, so flexing the telescope didn't wander the spectrum across the detector. Scrambling in the fibre evens out the light, too. Lyra, I'd never have guessed the trick was a cable.