Answer: You can apply directly to MOH if you are already in Kuwait but if you are located in some other country then you have to go through some agencies nominated by the MOH.
While you will have to forward the applications through the nominated agency, the examinations and interviews are conducted by the MOH delegation itself.
This responsibility is not delegated. If you are in Kuwait, then you can find out the date of the exams in Kuwait directly from the MOH.
Then you can sit in these exams and if you pass, you will be called for an interview. If selected, you will be asked to sign a contract.
Please remember that a lot of unscrupulous people are nowadays involved in the recruitment industry and various Kuwait ministries are trying to weed them out.