They want the Ukranian government to enter into an agreement of cooperation with the EU (a first step to becoming a full member).

Putin doesn't want Ukraine joining the EU since it would put "Europe" right on the Russian porch, whereas Putin would prefer to have a buffer of client-states who take their orders from the Kremlin. Ukraine gets most of its energy supplies from Russian natgas, which has been the main "stick" Putin has used to get the Ukraine to toe his line.

They think that best way to democracy is topple legitimately elected government.

That happend yesterday at 5a.m. police have bitten peacful protestors to clear main capital's square in order to set up christmas tree there. That lead to huge amount of people gather on streets of Kiev today. And small group of provoker tried to get into Presidet's Office as seen on different ustreams like this ones.