To gain entrance into an MFA program, you will need to get an undergraduate degree in art from a college, university, or art school, and be able to demonstrate your artistic vision, talent, and skills through your art work. Gaining employment as an art professor is very competitive, and rarely do you start our as a full professor, but usually as an instructor and work your way up. Advancing to become a full-tenured professor takes time and hard work, and having your work exhibited in galleries on a regular basis can also be important.
So, the steps start early, and it is a lot of work. If you are in high school, take art classes and talk to your teachers about building an art portfolio that will get you into art school, or help you gain admission into a college or university with an art department. Keep your eyes open to what is going on in the art world. If you can, got to art museums or art galleries. If you aren't near a museum, you can always visit museum websites, and of course, checking out art on Pinterest or Instagram is also an option.
If you like the idea of teaching art and like working with kids, another route is to teach art to elementary, middle, or high school students. I taught art in middle school, and I loved it. Getting a job as an art teacher in elementary and secondary schools is less competitive than getting a job teaching art at the college level. To teach in public schools, you'll need to earn a teaching certificate or teaching license. Depending on the requirement of the state where you live, you'll need at a minimum a Bachelor's degree in art education, but many states now require a masters degree as well. I had an undergraduate in art history, and I got a masters in Art Education. It is very rewarding career, and from what I understand, the salary and benefits match, if not exceed, those of teaching at the college or university level. Of course, your students will be very different, but if you like work ing with kids, then I'd check this out. Contact the National Art Education Association (NAEA) for more information about teaching in elementary and secondary schools.
Best wishes! Hope this helps.