The closest airport is Domodedovo 69 km from the city. The cheapest way is to take bus that goes to Domodedovo and get off at Vzletnaya stop. Then, take a train that goes north not Moscow. The time on train is about an hour.
By car
By car
M4 road will take you to Stupino from Moscow. Distance is 88 km. The road is stright, without any traffic lights. Traffic police check stands near Mikhnevo.
By bus
By bus
Bus #334 goes hourly from Krasnogvardeyskaya metro station in Moscow starting 8AM and the last bus departs at 9 PM. Very dependable on traffic. The price of a ticket to Stupino is 145 rubles.