Your question is vague. What's your role in the project? I've worked on a lot DOT projects, the specs list the safety requirements, eg, competent persons, demolition and erection procedures, comply with OSHA, no drinking or drug use on the site; PPE, porta-Johns, etc, and require the contractor to submit a plan explaining how they will comply with said requirements. It's the contractor's responsibility to ensure that his work force complies with the requirement. The specs give the owner's representative the authority to stop any part or all of the work if the contractor is violating the safety plan. Of course, OSHA can walk in at any time unannounced and issue citations or shut things down independent of the owner.
If you're on the owner's side of the fence, your contract has to spell out the safety requirements. If you're on the other side, you better have a safety program in place. Not only does it save you money on worker's comp premiums but you don't want OSHA coming down on you.
The only person who enforces safety regulations is the government representative for workplace safety. Everybody else is to comply and outperform. The most important tool in a workplace safety program is verbal 2-way communication and lots of it. Your question indicates this could be a good starting place, regardless of who you are.
Well it's a very vague question and with no context, but training and encouragement is by far the "best way" to improve safety.
Only when the people actually exposed to the danger understand what the risks and consequences are for them and their fellow workers and how to prevent it will you get serious improvement.
"enforcement" needs to go hand in hand with that, but can then become counter productive and you don't get people reporting all the near misses for fear of punishment or censure or loosing their job.
Only by bringing the workforce with you can you get to a good place.
You can include contractual requirements and inspections all you want, but there needs to be the push from the bottom up as well as the top down. IMHO.
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
