On the trains, you can go for 3rd class (platskartny) or even a seat, instead of a kupe.
Eat in local food joints rather than international-looking food restaurants.
Get a SIM card to be always connected (wifi networks require a valid SIM number for logging in). I use MTS, it works in all Russia. All you need is your passport on the moment of purchase. I usually pay around 500₽ to 700₽ for 30 days, up to 20Gbs of data.
Get a Troika card to travel on the metro in Moscow and Saint-Petersburg.