No dialects in Russia. Just NO DIALECTS.

(it's not regarding those whose mother tongue is not Russian, as Kadyrov, the president of Chechnya).

The only noticeable feature in speaking is unstressed "o" pronouncing exactly as "o" (not as "a" like in the standard Russian). It's the region in the northeast against Moscow: Kostroma, Yaroslavl, Vologda. By the way, educated (say, "posh" ) people speak standard Russian even there.
Also, in the south (Sochi, Krasnodar krai) and, I think, in the areas close to Ukraine some people pronounce "г" as Ukrainian "г".

If you'll ever read any tales about differences about Peterburg and Moscow speaking, stop reading that rubbish. Those differences really existed, but now they don't. Moscow and Peterburg inhabitants speak identical. The same is true for almost the whole Russia, actually.

P.S. When I see on TV people from Ukraine or other former Soviet republics speaking Russian, very often they sound completely like any of my neighbours to me. If I am not mistaken, the prime minister of Armenia sounds like a common Russian to me (and the President of Armenia has a noticeable accent, but anyway his Russian is very good).