Could anyone provide a site to download NDVI images or raw satellite images of Sri Lanka (Asia) for free for me to calculate the NDVI.
For high spatial resolution, you can download Sentinel-2 data. It has worldwide cover every ten (very soon 5) days. You have 10 meter bands in Red and NIR, so you can compute ten meter NDVI (vs 30 m with Landsat). Make sure that you use the L2A images (radiometrically corrected with SEN2COR) in order to compute a meaningfull NDVI value from the "Top of Canopy" reflectance (NIR-Red)/(NIR+Red).
Primary download site for Sentinel
alternative solutions can be found on Where / How to download Sentinel 2 Images
If you are more interested in the temporal resolution than in the spatial resolution, daily images are available from Sentinel-3 (soon), PROBA-V or MODIS. Again, I recommend using TOA (level2) images.
PROBA-V : http://aida.vgt.vito.be/content/products
MODIS (and also Landsat, but for Landsat only you could use Libra as mentioned by @Richard Law): https://earthexplorer.usgs.gov/
Libra provides a really intuitive interface to obtain Landsat imagery according to various spatial, temporal and image-suitability filters. I highly recommend it over EarthExplorer.