To start an NGO you have to get it registered. It can be registered as trust, society or a Private Limited Non Profit company. The NGO should have the following criteria met.
1.It should be an independent Organisation
2. There should be a board of trustees or Managing Committee or Governing Council.
3. It should work for the help of non members of the Organisation. That means it should work for the benefit of outside people.
4. The Organisation should not have any profit out of these activities.
Once they met the above criteria they can be registered in any one of the above mentioned categories
In addition to the above some NGOs require special licences as described here under.
1. If the Organisation is having a place of work in a restricted area, it requires permission from Ministry of Home Affairs or District Magistrate. I think for the mentioned NGO this permission is required.
2.If NGO wants to have an office and employees, it should be registered under shop and establishment acts.
3.If NGO is planning to employ foreigners permission from FCRA and NOC from DM is required
4. If NGO is of foreign origin and wants to to have an office in India and want to have foreign employees a permission from RBI and NOC from Ministry of External affairs are required.
I don't think government will give any financial support from their side. You have to pool up the required finances. You should have some like minded people who are willing to join as members either from your friends and relatives or outsiders. You have to maintain a good record of all your accounts, financial activities, events conducted, source of income and expenditure details.
You please think on these lines and try to take the opinions of other possible partners and then start the registration process.