Open Logistics → Rate Areas and click New Rate Area.
Name — for example Rest of India. Set Type to Shipping.
Under Geographic Zones, click Add Zone and choose the Country, and optionally State, City or Postal code ranges. Use * for "all". Add as many zones as you need.
Min Order Amount — optional minimum order to deliver to this area. Leave it at 0.00 for no minimum.
Set it Active and save.
Tips
Start simple: one area for your own city or state, one for the rest of the country.
In a shipping method you can also use Default — all other destinations, so addresses that match no area still get a price. Leave it out if you don't deliver everywhere.
The countries, states and cities you can pick come from Settings → Countries, States and Cities. Switch on a country there before you can deliver to it.
Rate areas of type Tax are used for tax rules, not shipping.
