Consulate
Since Citizens of India are not eligible to enter with just a passport and tourist card you'll have to have a visa, so you need to find and apply at a Dominican Consulate or Embassy with consular services.
And if you connect in a country that does not have connecting flights arranged so you don't clear immigration in that country (unlike the US and Canada, where you have to clear their immigration) you will need a visa for that country too, either tourist or in transit.
There don't appear to be Dominican Embassies or Consulates in India, the nearest seem to be in Korea or Japan.
This seems to be a pretty daunting request you have here.
