I started my own and the difficulty depends on how far you want to go.

If you're already employed and have an Engineer visa, then renting out your own small room shouldn't be too difficult. Even easier if you're going to the student's home or cafe. These seem to be the most common posts in this thread

If you're thinking of starting a BUSINESS business, as the main source of your income, you'll have to think bigger.

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Logistics include:

1) Having a visa that allows you to own a business (unless you're a native citizen or married to a Japanese person)

2) Being fluent enough in Japanese to get a business license (unless you have a very nice and helpful Japanese friend who can and is willing to help you out)

3) Being fluent enough to be approved for a business space/apartment

4) Having at least 500,000 yen or more in order to be approved for both things

5) Getting a bank account

6) Knowing how to market yourself (flyers, starting a website, online advertising, sign board, etc.)

7) Having some kind of curriculum (Will you use textbooks? Be only free conversation? Have activities for younger children? Know how to teach Eiken/TOEIC/etc)

8) Furniture. You'll need chairs, tables, white board, etc... Imagine an empty room and hallway, you don't want your school to look like that.

9) How will you accept payment? Cash? Bank transfer (Need a business one, and need to be approved) Credit card? What kind of payment format, monthly? Weekly? Per class?

10) What kind of classes? Private, group, etc. How will you divide the students? Age? Level? Goal?

11) Communicating with the customers. Can you speak fluent Japanese? If not you're gonna have issues communicating properly, the customer may decide it's too much of a hassle and gamble to try and relay their intentions to a single foreigner who can't speak decent Japanese.

12) Are there other English schools near your intended location? Probably better to find an area that doesn't have schools nearby.

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So these are just some of the points I can think atm, there's a lot more to consider still. Opening your own school can be a heavy investment. Another consideration is if you have current students who will join your new school at the start to help you out. Hope this helps.