There are numerous airlines that carry passengers daily from India to the country of Bhutan. Two of the major flights which have a direct landing at Paro include the Druk Air Flight as well as Bhutan Airlines Flight. From that location you can take a taxi which would leave you in Punakha district.
No Visa required by the citizens of India.
You can visit the district of Punakha by travelling through numerous inter-district buses which travel form the border of Phuentsholing. Numerous private buses with the seating capacity of 22 run through this area.
In case you wish to reach Punakha by Air, then you would have to take a flight to the Bhutanese International Airport and from there you can hire a taxi or take an intercity bus which would take you to Punakha.Search for flights to Paro
You can reach to the Bhutan International Airport which is located in Paro. Here you would be able to get a taxi which would leave you straight into the district of Punakha.
You won't be able to reach Punakha By Train as there are no train services
There isn't any route to Bhutan by Sea.
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You can mostly travel through this area on foot. However, if required then there is a taxi stand near Dzong where you can hire a cab for going to any place you like.