Polling in Russia was done by the Levada Centre and from their website, I took the following:
Levada Analytical Center (Levada Center) is a Russian non-governmental research organization. The Centre regularly conducts sociological research. Levada-Center is one of the largest Russian centers in the field.
Staff of the center brings together experts in the field of sociology, political science, economics, psychology, market research, public opinion polls and organization of data processing. The team is guided by the principles of WAPOR and ESOMAR.
Senior staff have been trained in the USA and Western Europe. The research team has been conducting regular public opinion polls across the country since 1988.
Levada Center has the network of 67 regional offices and maintains partnerships with centers of public opinion research in the CIS and Baltic countries.
Polling results and expertise of the Center’s staff appears is broadly covered by national and international media such as Kommersant, Vedomosti, Gazeta.ru, the Economist, The Wall Street Journal, The New York Times, Reuters, BBC Radio, Radio Liberty, and others.
https://www.washingtonpost.com/news/worldviews/wp/2015/06/24/putins-approval-ratings-hit-89-percent-the-highest-theyve-ever-been/
http://www.levada.ru/eng/levada-center The group that did the polling
As it is a non-governmental body it isn't required to adhere to Kremlin propaganda and apparently it's research is acceptable to the standards of the Economist, The Wall Street Journal, etc.
Also, contrary to popular ideas, the Kremlin doesn't force everyone to 'say nice things' about them. I read the Moscow Times periodically and they regularly criticize and print unflattering stories about the current government.