First, know that there are a few basic requirements for anyone in this field. You need to love fabric and sewing, and the act of creating something. You also need to be precise and a perfectionist. A good tailor just won't create a so-so garment. Add in a need for decent mathematical skills and basic bookkeeping and you'll see that not just anyone can get this kind of job. Tailors have to be able to follow instructions precisely, while using their own judgment to create a garment that will fit the person they're making it for - not an idealized form.
It's a good idea to get some schooling, either at a fashion and design school, or as an apprentice to a skilled tailor who's already in business. Don't make the mistake of assuming that a tailor is the same as a designer. Tailors generally work on the construction of clothing, not the initial design of high fashion. Most won't even be involved in fitting the pattern to the person who's going to wear it or in cutting out the fabric. Those are separate jobs in many shops.
Remember that this isn't a field you can just jump right into. Tailoring requires years of experience and practice. You can start with your own clothing, or that of friends and family, or get some minimal training with a local alterations service. But don't stop there. Work on higher end garments and learn all you can about how to construct anything and everything. After all, you never know what you'll be asked to work on. Don't dismiss old fashioned techniques just because they're old, either. Many of them are required if you want to make a traditional suit or several other types of garment.
Most tailors will specialize. While it's a good idea to have general knowledge of most types of sewing and garment construction, you'll probably find that you get most of your work in just a few areas. This is particularly common for tailors who've apprenticed. They'll tend to see the same kind of work as their masters. It's important to become extremely good in your area of specialty, and to know the ins and outs of how to fit many different body shapes. Being versatile and experienced is important for anyone who wants to succeed in tailoring. Taking shortcuts or assuming you know everything will be disastrous.
Being a tailor can be an extremely rewarding job, if you've got what it takes. You have to do more than just a few fittings, or know how to hem a pair of jeans. The job takes attention to detail, a willingness to practice, and an unwillingness to send out garments that are less than perfect. Plus, you have to be willing to keep on learning throughout your whole life. However, if you take the time to do this, you'll find that this is a wonderful career. There are great opportunities out there in tailoring - after all, many people still realize that a custom fit, hand made garment is worth the extra cost.
If you're interested in becoming a tailor, start learning now. Find out what your preferred interests are and look for someone who can help you get the skills and knowledge you need. It's worth it in the end.