Finding hotel accommodation in large cites is typically not a problem - there are enough places to stay, from modern five-star hotels to old ugly guesthouses that have not been refurbished since USSR has fallen apart. The prices are unfortunately not that cheap as can be found in South Asia, you will probably never find anything below $10 per night.
Russian countryside is not a particularly hotel-overloaded zone. In the medium-sized towns you're likely to find just one or two guesthouses and in smaller towns and villages there will be nearly nothing at all. Exceptions are holiday destinations - like ski resorts in the Caucasus, fishing camps in Karelia, recreation centers in the Altai and so on. The problem is that you rarely come across right place just when you suddenly need one in the evening - you have to know and plan beforehand.
The situation is more favorable in the Central Asia - people here used to travel a lot and to stay along their routes. You should be able to find at least a basic place to stay almost everywhere (tea houses are the best spots to ask for). In many places, especially in Tajikistan, it is a custom to stay in private houses and most people in remote villages will be invariably pleased to invite you as a rare guest and to offer you the best food they have.