The reason someone is unable to perform a push-up is due to the lack of strength in the three major muscles required to perform a proper push up. Those muscles include the pectoralis, deltoids and triceps.
Having your client perform various exercises that help strengthen these muscles should eventually allow them to build the strength and balance needed to properly execute a push up.
Depending on where your client is at his/hers strength training this could take a couple weeks or a few months. Working with light bench press, shoulder press and resistance bands will help build their strength to the required amount. Remember not to rush it since an injury would be detrimental to the progress.