Contrary to what this person is called, they do not just make cabinets. This person works with wood to design various types of furniture. If you enjoy working with your hands and crafting things, this might be the ideal business for you. You also must enjoy working with furniture that involves a lot of detail work.
You should check about getting a certificate in "Furnishing-Furniture Manufacturing," which consists of three levels of courses that you can finish in about a year. You can find them through your local woodworker unions. There are even some colleges that offer these courses. By the time you are finished with this course you will have an understanding of cabinet construction and design basics, wood processing and refinishing wood.
If you prefer, you can take some woodworking courses at the community college. These classes normally focus on some part of being a cabinet maker. If you know of someone who does cabinet work or any type of woodworking, see if you can get a job there, even it is volunteer, to get some hands-on training.
If you just want to do it by trial and error you can always go to your local library and check out some books on woodworking. Start out small making jewelry boxes, trinket boxes, or other small items. You can take these small items to a craft show to sell.