Accomplishing the exoplanet science enabled by TESS requires follow-up of many transiting planet candidates throughout the entire sky, to identify false positives (FPs) and confirm real planets. An efficient follow-up requires a global facility and a large amount of telescope time. This Las Cumbres Observatory (LCO) Key Project is designed to do just that, with about 2,500 hours of telescope time per semester for 6 semesters, 2020B - 2023A. LCO telescopes are fully automated, including 10 x 0.4m, 11 x 1.0m, and 2 x 2.0m telescopes in 7 sites. We are using all LCO telescopes, equipped with imagers, and we also have time on the high resolution NRES spectrographs, installed in 4 sites. Imagers are used to observe the TESS candidates during transit and check if the transit signal seen in TESS data originates from the target or from a nearby star blended with the target in the TESS wide pixels and wide PSF. The NRES spectrographs are used for measuring the stellar parameters of bright TESS candidate host stars down to 10th magnitude, identifying obvious FPs (SB1, SB2), and measuring the orbits of massive planets. This Key Project is part of most TESS planet discoveries. We present our methodologies and some of our discoveries.