I normally prefer trains, but Moscow and ‘normally’ do not work well together. So for out-of-town excursions I now use coaches – they are modern, comfortable and fast (unless you are caught in the traffic).
No random disorderly seating, you are seated according to your ticket, there is a luggage compartment, there is even a hostess with snacks and tea (don’t recommend, honestly - you'll spill it on your knees).
It’s 240 roubles one-way, and 40 roubles for the luggage, if you have any.
For the bus station in Moscow go to Vykhino metro station (purple line, southern direction, last stop)
In Kolomna go to Golutvin bus station (NOT the 'Old Kolomna' bus station near the Kremlin!)
The buses go every half-hour, will supply the schedule and the map once – and if - I have time.
Take a local train from Kasansky Voksal in Moscow. The journey takes about 2,5 hours one way and costs currently 104 roubles one way to Golytvin. If you want to see the old part of town first, then get off at Kolomna station.
Make sure you look out of the window to your right when approaching the town, so you see where the sights are located.