[Physicist]

Or, just guessing,

C. Looked at the whole spectrum and picked out absorption lines that exhibited a Doppler wobble with respect to the emission lines as the planet moved around the star.

[RadioAstronomer]

Beat me too it! :)

[steve-b]

C. Looked at the whole spectrum and picked out absorption lines that exhibited a Doppler wobble with respect to the emission lines as the planet moved around the star.

Er, no. If the planet is directly between the star and us, its radial velocity is close to zero unless it's in a very eccentric orbit.