Question

How are the responsibilities and function divided between the different tiers of government

Answer 1

by horizontal division of power and vertical division of power

Answer 2

The differentiation and division of the responsibilities of the state and central government is specified in terms of Three Lists in the constitution of India. 

1. Union List
This list contains 100 items of national importance on which the central parliament has the exclusive rights to make laws. The topics included in this list are of national importance and require a uniform application throughout the country like Defense, Currency, Banking etc.


2. State List
This lists contains a list of 61 items on which the state governments have
the exclusive rights to make laws. These topics pertain to day to day governance and which can be legislated well locally. Thus we have topics like Police, Agriculture etc. coming in this category.


3. Concurrent List
This is a list containing 52 items on which both Central as well as State government have the rights to make laws. In the case of a conflict, the laws made by the central government prevail. These are the topics which cannot be put in the above two categories and are of interest both locally as well as nationally. These includes Criminal Laws, Forests, Marriages and Divorce etc.


Apart from these, the topics which are not covered in these three lists (which became prominent much later when the constitution was being drafted like software and information technology) are included in the residuary subjects on which Union government has the sole right s to make law.

There are exceptions to these rules in some cases like Union Territories (Delhi, Lakshadweeep etc where Central government has direct control) or a state like Jammu and Kashmir which has a special status and a constitution (even a flag) of its own.

PS: I am not sure about the coming part. My history teacher told the same when I was in school and I still remember it. Feel free to correct me, if I am wrong.
Lastly, I would like to add that the balance of power in India is slightly more tilted towards the Central government to account for the great diversity and conflict of interest between the states divided on the basis of culture and language. This helps keeping India intact, functioning and well as we know it.