It depends on at what level you wish to coach and to how high a level you want to succeed.
There are beginning coaches who have no professional background in coaching. They usually coach summer league recreation teams. They usually coach from what is called "the seat of their pants" which means that they do what they think is right but don't really know why or what they are doing.
Then there are coaches who understand motion, levers, hydrodynamics, muscle function, blood chemistry, nutrition, nerve function, psychology and many other things. Such knowledge allows a coach to become creative and to develop skills and techniques that will aid her/his athletes to reach potentials.
If you want to achieve at a high level, you'd go to college and major in kinesiology and/or exercise physiology. Although it is not 100% necessary, you'd want to compete in college, too ... preferably for a coach who has a high level of success. Doing these things should teach you the reasons for doing what you do and provid you with techniques and skills for coaching.
You should start your career as an assistant coach. The "greater" the head coach the better.
If you coach in high school you'll need the basics of having some experience in the sport as a coach or participant. It is preferable that you have a college degree that includs a minor in kinesiology/exercise physiology.
If you coach year round age group consider that most such coaches are professional coaches and that is their only job. The pay is not great ($24-$48,000 per year) but, if you consistently produce great swimmers, some year round coaches (and college coaches) earn $100,000/yr.
Professional coaches that coach age group swimming must also attend specific classes offered by United States Swimming (USS) AND show competence in their application of the knowledge they've gained by producing fast swimmers. Coaches are then assigned a level of competence of between Level 1 to Level 5 by USS. A USS Level 5 coach consistently has kids who are world class swimmers.
Finally, for all types of coaching, most employers require the coach to maintain CPR and First Aid certification. Some employers might also require other related certifications such as life guard or water safety instructor.
Good luck! I've been coaching for about 30 years. I was very fortunate to have swam for a coach who wrote a book that is recognized as the greatest book on swimming ever written. I learned many things by being an assistant coach (3 years) for him. In addition, I've expanded my education as described above.
The book is "Swimming Fastest" by Dr. Ernest Maglischo, PhD in exercise physiology. The book is extremely scientific in nature and goes into in depth explanation of all aspects of coaching swimming. It is available on line. Try google.