Under normal circumstances, you would need to show the airbag should have deployed but did not. You should prove the airbag is defective, and you obtained injuries because it failed to deploy. Your injuries would need to have led to financial, physical, and emotional damages.
Sometimes, airbags will not deploy if the impact is severe enough. You would need to hit a solid wall or tree at 16 miles per hour or higher. Otherwise, you would not be able to sue for damages. If you were driving under the influence, the airbag manufacturer might use it as a defense to avoid liability, especially if there is a DUI. It can help to consult an attorney to determine the next step.