The main thing is not to panic and not rush to fill up your tank ahead of time. Gas prices don't fall as quickly as they rise, because gas stations already have fuel purchased under old contracts. Retail margins also don't allow them to cut prices sharply, even if wholesale prices have dropped.
The mechanism itself is straightforward: a low demand forecast means that oil-producing countries are less actively buying it going forward. This puts pressure on the barrel price, and after some time the effect reaches retail. But "after some time" doesn't mean tomorrow. Usually there's a lag of several weeks between movements in international oil prices and cheaper gas showing up at the pump, sometimes longer, depending on how quickly fuel from cheaper batches makes it into retail networks.
It's better to track this not through news about forecasts (they're often overblown in the press), but by actual oil quotes and by looking at how gas station prices changed a month or two ago. Historical trends usually show how strongly and quickly retail responds to price movements in a particular region.