very well explained by johngan!
I think if you have GPS points with locations of paddy crops, you should somehow add another 50 points at locations where no paddy crops are expected. Having these 100 points, you can calculate a small buffer around them (GIS) in order to include a bit more pixels. Then you use these 100 polygons for training the classifier as explained above. They should have an attribut column with 1 at paddy and 0 at no-paddy, for example.
Importing shapefiles in SNAP is explained here: Can't import vector data
But the suggestion about the color composite of a dual-polarized scene is a good start to get to know what SAR data is able to offer for your analysis.