You need to find someone to mentor you and apprentice you, and that usually means paying your dues first.
Also, dog training is ALL about the people. So if you are not prepared to better yourself, work hard, and be uncomfortable for a couple years until you get your confidence, then this is not the work for you. BUT if you are willing to put all excuses aside, work hard and work on yourself, then you can go as far as you want.
Dog training is rarely just teaching a dog - you need to teach the handler. You need good communication skills, the ability to relate to people and the ability to convey what you are trying to achieve.
I started out with my own dogs, then fosters - then I decided I wanted to be a dog trainer. Then I had to learn how to operate as an extrovert (I am introverted) and even after 8 years, I still struggle with becoming exhausted after 4 hours of classes, because I draw energy from being alone. It was the BEST decision I have ever made - and the hardest.
My first tip - stay humble, never get too cocky and ALWAYS be willing to learn something new.
Find a trainer who trains in a style that you would like to work with (This can change later on), get in the classes, show that trainer what you can do, and build a relationship with them. If you are really good, chances are they will ask you if you have any interest in the field.
Look up clubs in your area (and outside too) who host seminars with trainers/judges/competitors in various areas, and get in on them. You will always learn at least one thing new. Use your dogs, they can always teach you more.
This is how I started 2 years learning the style of training I wanted to train, then 2 years being the "helper/Janitor/equipment hauler" etc, then 6 years of learning to teach classes of up to 15 students (Obedience - 7 Levels, Protection, Tracking, Rally'O, Agility etc) and now after 10 years I am travelling to Hungary to earn my certification through the FCI and this summer I will start teaching my own classes (Flyball, Kyaking, Nosework etc).
My FAVORITE part of this "job", is when you meet someone who is at their wits end and ready to 1)Euth their dog or 2) give it away. You spend a few weeks showing them the possibilities and (dog dependant) then a year (or two) of HARD work and when they come to you and say "OMG! I love this dog and I actually ENJOY spending time with him/her" - that is the best feeling, that I helped create that.
If you decide you only want to work wtih dogs - the shelter/rescue route is a good one. You could "prep" dogs for adoption and increase adoptability.