What steps should be taken by an organization to create safe environment for their workers?

The organization will ingrain the concept of safe working environment into its very culture. The procedures and processes alone will  already reflect the company's initiative to maintain a safe environment. The management will communicate these to all, and supervisor will include such discussions in meetings. The new employee onboarding / induction will emphasize this so the employees themselves will behave in a safe way and to maintain a safe workplace. The actual workplace will be designed / renovated in a such a way that promotes it. There will be an assigned trained first aider among the staff, or a nurse if the company is larger, and with ample first aid kit and medicines. Employees will be informed on emergency procedures and contact details., and will be regularly trained on emergency drills.

Most important way is to communicate with the team and get them all on board. In specific, weekly safety meetings would be a great practice!