In case you don’t have your own wheels, the trains are always come to the rescue – there are two options, both leaving from Moscow’s Kazansky Vokzal (at metro Komsomolskaya on the red/brown line):
Express train: there are three per day in both directions heading for Ryazan, but stopping at Golutvin which is a couple of km from downtown Kolomna – walk from there or catch a cab for 100Rbl. This option is definitely the quicker as the train takes around an hour and a half and you’ll have a reserved seat, but tickets can sell out at peak times. Unlike the elektrichka, once the tickets have gone, it’s tough luck – you’ll have to wait for the next train (unless you’ve booked in advance)!
Elektrichka: there are numerous trains daily although bear in mind that they stop at every lamppost along the way so the journey will take you over two hours each way. Buying a ticket doesn’t guarantee you a seat and in the summer months you’ll share a wooden bench with a babushka carrying two large bags to and from their dacha. The advantage of this method is that the tickets are (slightly) cheaper than the express, and they don’t sell out, even if you have to stand for part/all of the trip, and the train will drop you off right in the middle of Kolomna!