Where to Begin
Sometimes the hardest thing about dream jobs is figuring out how to get them. Often the best way to start is asking someone in the field how they got their start. This is where I can help, as an aquarist I know what it takes to break out into the zoo and aquarium industry. My advice is simple: school, volunteering, internships, apply for everything.
No matter what you want to call yourself, keeper, aquarist, or trainer, school is important. Is a college degree needed to work with animals in a zoo or aquarium setting? This is a hard question. Technically the answer is no, but it does help set you a part and show that you have good work ethic. Now that you have decided to get a degree what do you get?
Many people working in zoos and aquariums have a degree in biology or zoology. If you want to be an aquarist it might be more beneficial to consider marine biology as a major. If animal training is more of your goal then you might want to consider psychology. Each major has its pros and cons. For example at most schools biology programs cover a wide range of topics: cell biology, evolution, botany, zoology, ect. Specializing in a more specific major (marine biology or zoology) allows you to focus your studies in your field of interest. As far as having psychology as a major you need to be aware that most schools present psychology from a human perceptive and you will be learning a lot about human disorders as well as the principles of behavioral training.
Almost as important as picking a major is choosing a minor. Personally I found that A major in Marine Biology and a minor in Psychology best fit my needs. I figured it would give me the knowledge I needed about marine life as well as learning how the animals think and learn. I was also insuring that I would be able to get a job with animals in another setting if I couldn't find a job as a marine mammal trainer (which I did not). There are a wide range of minors found in this field: scientific technical writing, geology, business, Spanish, and physics are just a few. Just like with majors there are plusses and minuses to each minor.
When it comes down to it choose a major and minor that you are passionate about. It also doesn't hurt to entertain the idea that most people that set out trying to get jobs in zoos and aquariums are not successful and to choose a major that will allow you to get a job doing something you would like doing. Think about it; if you couldn't work your dream job in a zoo would you rather sit at a desk and answer phones or would you rather work in a lab?
Volunteering and Internships
One of the best ways to get your foot in the door is to volunteer. Too often young people do not take this advice. My question to you is how do you know this is what you want to do if you have never done it? Sure most kids have dreams of being a dolphin trainer when they are young, but most never do. A good number find out, through volunteering, that it isn't just playing with dolphins and having fun all day.
Many facilities allow volunteers to work with the exhibits staff, typically the magic age is eighteen. As a volunteer you will typically learn the food prep for the section you are assigned. As the staff is able to trust you, and as you learn the job, you could get more tasks and possibly hands on experience with animals. Going back to the dolphin trainer example it is almost sad how many volunteers never come back after their first smell of food prep. This is not a glamorous job. You will get dirty, you will smell, you will be hot/cold, and most likely wet for most of the day. Wouldn't it be better to find out that you don't really want to work as a keeper before spending all of your time and money getting a degree for a job you don't even want? Of course it is: volunteer. It doesn't matter if it is a zoo, aquarium, veterinary clinic, wildlife sanctuary, or a local farm, just volunteer.
Another great way to gain hands on experience in this field is to intern. Most facilities require interns to have a year or two of college under their belt, some even want previous volunteering experience. The main difference between volunteering and interning is that interns are typically given more responsibility than volunteers. Interns may be allowed to dive in exhibits, participate in training sessions, design new enrichment pieces, and so on and so forth.
It is strongly recommended to do at least one internship before leaving college. Kind of like with friends the more the better. A lot of facilities want their potential hires to have volunteering experience, a college degree, and at least two internships.
Now that you have a degree, a couple of years of volunteering, and an internship or two what do you do next? Apply for everything. It doesn't matter if it isn't exactly your dream job apply. What is the worse that will happen: you never hear back. Best case scenario you will get an interview, or even better a job. You will most likely complete dozens of job application for every one interview you get. That is normal. Trust me, this is not a job you just get overnight. It takes time.
If you are not one of the few who are lucky enough to get a job right out of college don't worry. It isn't all that uncommon to have a year or two between college and that first job. In the mean time continue to volunteer, apply for the internships you are still qualified for. Don't give up! If you need to move back home with your parents and get a job in retail do it. Whatever it takes, this is your dream after all.
Things to Keep in Mind
One really important thing to keep in mind is that this is not a field where you will get rich. The pay is typically around minimum wage and jobs are hard to come by. This is a field that you do because you have a passion for animals and a dedication to giving them the best care possible.
It will also be very hard, most likely, to get your foot in the door. If you are lucky enough to get a job chances are pretty good you will start with part time and have to work your way up to full time. That's just how it is in this industry. Typically it takes at least two years of experience before most facilities will even consider you for a full time position. Its though, I know. Stick it out!
Its often painful for some interns to grasp, bust just because the group of people you intern with really like you and you do a great job does not mean that you will get a job at that facility. The vast majority of zoos and aquariums are run by a government: city, state, or national. They can't just make jobs appear because they like you. You will have to wait for one to open. In the mean time apply for everything! That way when a job does open you might have some interview experience, or even paid experience in the field, to help you get your dream job.
Best of luck!