Russian government does censor the internet. There is a blacklist maintained by Roskomnadzor; it, for instance, blacklists certain Wikipedia pages, along with certain opposition and other "extremist" web sites. Russia lacks a China-style single-choke-point firewall; ISPs have to enforce it.
If you have a chance to watch any Russian TV, you can't avoid noticing how propaganda-heavy it is, and how all the propaganda is in favor of the government (in the US, at least, the latter is not the case).
Also, being a businessman of any importance and not following the party line does not work. Not all cases are as dramatic as Khodorkovsky's, who happened to own one of the largest oils and gas companies, but legal harassment of business for political non-conformance continues, or continued while such non-conformance lasted, or, at least, was publicly visible.
This is milder than China, and way milder and more sane than than the Soviet regime was; there's no doubt about it. Also, the sharp rise in living standards of 2000s, fueled by oil prices, is still remembered and has not completely deteriorated. So Putin does enjoy some genuine citizens' support. It's still not something that citizens, acting freely and with consideration, have chosen, kind of like the Swiss do in their referenda.