How difficult is it to start a career in dentistry?

It is a long, sometimes hard road. But you'll probably find that is the case in any profession requiring post-baccalaureate training.
Let me be clear--from my perspective over almost 40 years out, it is not so rigorous intellectually to get through dental school. That does not mean you can sleep through school. As with most things worth working for in life, you will get out generally what you put in. And school itself is a grind.
It is hard to make broad sweeping statements about what you will find after school, because the potential areas open to you are far wider than most people will imagine. Although most dentists eventually settle into private practice, quite a few don't. There are academic opportunities, areas of both academic and industrial research--and the research opportunities are very broad--because the variety of actual work in clinical dentistry is very broad.
Practice settings are changing rapidly. When I started the vast majority of dentists practiced solo or in small groups. This has become more and more difficult, and from what I see this is going to continue to change.
But--we're nowhere near the point where dentists won't be needed. When I was in college in the early 1970s, we were sweating that a vaccine against tooth decay was in early clinical trials in the UK. But it didn't pan out--and somehow people are still going into dentistry over 40 years later.
Spend some time talking to your dentist. Visit a dental school. Find out about the specialties of dentistry. Curiosity and a little legwork now will give you a big step up by the time you get to your first dental school interview.
Good luck!

Great question!

If you want to be a dentist, after college, you would need to apply to dental school. You can learn more about a dental school here: http://dentistry.umkc.edu/

To be a dental hygienist, you would need to attend less school, and would have lower earning potential. Information on dental hygene school is here: https://dentistry.umkc.edu/Future_Students/dentalhygiene.shtml

Dr. Bornfeld (above) makes some very good points. You can learn a lot by asking, searching the internet, and visiting schools and clinics. Most dentists are pretty friendly people. Dentistry was a second career for me. It is harder to be admitted to dental school than to medical school, as there are fewer places. It is a real grind during the first two years especially as you are taking all the courses that medical doctors take PLUS the dental laboratory classes. I do not know any dentist who denies having nightmares about dental school even years after school is behind them. It is a long, hard grind. But fascinating! and potentially very rewarding personally and professionally with many career paths possible. Good Luck!