First, he's a telepathic hypnotist (as in "I am the Master, and you will obey me"). He didn't have the power to control everyone directly, but, with the Archangel Network of communications satellites amplifying his power, he could at least influence them.
He's also a good politician. He appeared right when everyone was worried about alien invasions and the government was doing nothing about them. He became Minister of Defense, and he ordered the Army to blow up the Racnoss Webstar. When the Judoon took a hospital to the Moon, he cited this as a perfect example of why he was needed.
And he probably combined those two skills by hypnotizing influential people (from political leaders to Sharon Osbourne) to support him.