Question

how does non-green plants obtain their nourishment

Answer 1

they obtain their nourishment  by feeding on the decayed plants and animals.

Answer 2

The non-green plants are usually saprophytic or saymbiotic in nature.
Non-green plants like fungi may be saprophytic or parasitic. They cannot make their own food due to the lack of chlorophyll.
But they take food from other organisms or consumps nutrition from dead and decaying organisms. That is why they grow on dead and decaying
matter in damp and warm places to get sufficient nutrition.