Your Merit Badge Process starts with your Scoutmaster and ends with your Scoutmaster.
From the Boy Scout Requirements pp.22-23 via meritbadge.org:
You can learn about sports, crafts, science, trades, business, and future careers as you earn these merit badges. There are more than 100 merit badges. Any Boy Scout may earn any merit badge at any time. You don't need to have had rank advancement to be eligible.
Pick a Subject. Talk to your Scoutmaster about your interests. Read the requirements of the merit badges you think might interest you. Pick one to earn. Your Scoutmaster will give you the name of a person from a list of counselors. These counselors have special knowledge in their merit badge subjects and are interested in helping you.
Scout Buddy System. You must have another person with you at each meeting with the merit badge counselor. This person can be another Scout, your parents or guardian, a brother or sister, a relative, or a friend.
Call the Counselor. Get a signed merit badge application (blue card) from your Scoutmaster. Get in touch with the merit badge counselor and tell him or her that you want to earn the merit badge. The counselor may ask to meet you to explain what is expected of you and to start helping you meet the requirements. You should also discuss work that you have already started or possibly completed.
At the first meeting, you and your merit badge counselor will review and may start working on the requirements. In some cases, you may share with your counselor the work that you have already started or accomplished.
Unless otherwise specified, work for a requirement can be started at any time. Ask your counselor to help you learn the things you need to know or do. You should read the merit badge pamphlet on the subject. Many troops and school or public libraries have them. (See the list here.)
Show Your Stuff. When you are ready, call the counselor again to make an appointment to meet the requirements. When you go, take along the things you have made to meet the requirements. If they are too big to move, take pictures or have an adult tell in writing what you have done. The counselor will ask you to do each requirement to make sure that you know your stuff and have done or can do the things required.
Get the Badge. When the counselor is satisfied that you have met each requirement, he or she will sign your application (blue card). Give the signed application (blue card) to your Scoutmaster so that your merit badge emblem can be secured for you.
Requirements. You are expected to meet the requirements as they are stated -- no more and no less. You are expected to do exactly what is stated in the requirements. If it says "show or demonstrate," that is what you must do. Just telling about it isn't enough. The same thing holds true for such words as "make," "list," "in the field," and "collect," "identify," and "label."
The requirements listed in this book are the official requirements of the Boy Scouts of America. However, the requirements on the following pages might not match those in the Boy Scout Handbook and the merit badge pamphlets, because this publication is updated only on an annual basis.
If a Scout has already started working on a merit badge when a new edition of the pamphlet is introduced, he may continue to use the same merit badge pamphlet and fulfill the requirements therein to earn the badge. He need not start all over again with the new pamphlet and possibly revised requirement