I have just become a Permanent resident (got a green card) and would like to know
1. Since I got it in Dec. 07 (which is almost end of the year) do I qualify for filing worldwide income
2. I file taxes in India, how do I file worldwide income tax and how does it work ?

1) Yes, you must claim ALL of your world-wide income.

2) You file as a resident alien, then claim the Foreign Tax Credit (Form 1116) for taxes paid to India.