When can I trust my dog off the leash?

NEVER! Greyhounds have no understanding of cars. They tend to stand in the middle of the road watching the car approach, or they try to outrun it. They are sighthounds capable of speeds in excess of 40 miles per hour. They have been taught to chase fast-moving objects. Therefore, you need to structure a situation in which your dog can succeed and not be at risk; one in which you are in control. This may be an enclosed ballfield or meadow.

While basic obedience classes will give you good ideas for building a relationship, and could be really helpful for other concerns you may have, the instinct to chase will always override the learned command. This is also why greyhounds should never be tied to anything stationary outside. They can reach those fast speeds very quickly and could snap their necks.