(re)plumbing trap for double basin sink
The correct way is to have the trap directly below the tail piece from the basin that does not have the disposal.

You would cap or eliminate the Y fitting so you just have one outlet.

The disposal will connect straight over to the tail piece into a Tee ( baffled tee ) fitting attached to the tail piece and the tee will go straight down into the trap. 

Here is a basic YouTube video. 

How do you drain a garbage disposal?