I believe when Palpatine gave his speech in the Senate Chamber, he was using his Force Persuade abilities on a few select influential Senators (obviously he couldn't do all of them) to gather support so that the rest of the Senate would fall in line with the cheering/applause/etc. (obviously apart from Bail Organa, Padme Amidala, and Mon Mothma, etc.)
The Senate would not have picked up on his Sith robes - they were of obscure design and the fact that he has his hood up is explained by the fact that the Jedi 'made an attempt on [his] life' - he doesn't want to show the Senate his deformed face.
They were also war-fatigued and scared of the Republic collapsing, despite the war ending -- they were prepared to trade freedom for peace and stability, and as Palpatine had effectively 'won' the war (because by then the Jedi were being wiped out), he was massively popular with the Republic, so they had no problem allowing him to become Emperor -- notice, however, that he doesn't actually say HE will become Emperor, merely that an august leader, chosen for life, will be appointed.