Safaris are available from Dhaka,Khulna . Ranging from an overnight trip to a week, and are probably the best way to experience the Sundarbans.
Organizing your own trip from Munsiganj-Satkhira,Mongla or Khulna is possible and cheaper, if you're a shrewd negotiator, but questionably worth the hassle. You need a permit from the Divisional Forest Office in Khulna. With permit in hand, it's possible to hire a boat from Mongla or Dhangmari to get you to Hiron Point. From Hiron Point you will have to hire a guide to take you into the park.
Day trips from Mongla are not very interesting, and probably better avoided. After negotiating the price of a boat down to something only slightly less rediculous you'll most likely be taken to Karamjal Wildlife Center, where there are some tame deer to feed and some monkeys, crocs and snakes in cages. But surely you didn't come all this way to see a rundown zoo filled with depressed animals and raucous Bangladeshis. Boatmen seem to want no less than Tk 200 for the trip locals pay Tk 50/day, and the center charges a very steep Tk 750/day entry fee for foreigners.
From Kolkata India, suburban trains can take you to Canning 64 km from where launch services are available for Sundarban. Otherwise, you can avail of buses to reach Raidighi 76 km, Najat 92 km, Sonakhali 100 km and Namkhana 105 km from where motorboats will take you to Sundarban.