How do I rid moisture under my deck that's causing rotting of boards?
Plastic is okay underneath but not touching the deck's joists, i.e. on the ground. Put gravel on top to keep it in position. Secondly, ensure that there is a good airflow over the top of the gravel and under the deck structure. Never put anything between the deck structure and the decking material.

Ensure the ground is properly prepared under the deck structure/plastic sheeting by making sure water will not pool. I.e. slope everything away to surrounding ground or drainage.