Most of the people replying on this have suggested volunteering which I can agree with. It's how I started work at my current shelter. I suppose it depends on why you want to switch careers and if you've had experience with the world of animal welfare before, in any capacity. I don't know what the shelter/rescue, etc, near where you live looks like so I can't offer specifics. But if you've never had any experience with the field of animal welfare and you just feel the calling, I would highly suggest talking to someone at your local shelter about volunteering or even asking for a tour, if they allow it. Switching careers full-stop without having some experience can be jarring for some, particularly if your shelter has a low live release rate.
If you start volunteering, I suggest going in with an idea of what you'd like to do, but also keep an open mind to the possibilities. Some shelters have a limited set of things volunteers can do for them while others have a broader scope.
Our shelter has the basics, such as kennel cleaning and dog walking. But then we have volunteers who assist in our spay and neuter clinic, volunteers that work on our animal enrichment team, others that come in to take fancy pictures of our cats and dogs, some who do data entry for us, and even a very special volunteer who has dedicated an entire blog and Facebook page to our shelter dogs: finding them homes and delivering happy tails about the ones who have been adopted.
Also, when applying for a position or seeking to volunteer, keep in mind there is a difference between a rescue and a shelter, a government agency and a private one, and a small local shelter as opposed to one affiliated with a national organization (such as the ASPCA or the Humane Society of the United States). Simple things but they affect a lot about a shelter, from the funding they get to their reputation which in turn could have an impact on the experience you have with them.
#EducationandTraining