We gathered four reconnaissance spectra of TOI 540 with the CHIRON spectrograph mounted on the CTIO/Small and Moderate Aperture Research Telescope System (SMARTS) 1.5m telescope at CTIO. The observations were carried out between 2018 September and 2019 November in 3x20 minutes exposures per observation, employing the image slicer mode for a resolution of R=80000. In addition, we collected three spectra using the HARPS spectrograph mounted on the ESO 3.6m telescope at La Silla. The HARPS spectrograph has a measured spectral resolution of R=120000. The observations were carried out in 2019 April (ESO HARPS Program 0103.C-0442, PI: Diaz) with a 30 minute exposure time.Transiting Exoplanets Survey Satellite (TESS) collected photometry of TOI540 in observation sectors 4, 5, and 6, with the observations spanning a nearly three-month period from 2018 October 19 to 2019 January 6. Using the eight 40cm aperture telescopes of the MEarth-South telescope array at the Cerro Tololo International Observatory (CTIO) in Chile, we conducted follow-up observations of TOI540 to confirm the transits of the terrestrial planet. The MEarth-South telescopes employ a custom bandpass centered at the red end of the optical spectrum (similar to TESS). We observed 10 transits of TOI540b between 2019 July 27 and 2019 December 8, using an exposure time of 40s per measurement. (3 data files).