It is possible for anyone to set up a Sole Proprietorship at any time and there is no startup fee.
Except in the case of some outside employment prohibition created by one’s current employer, it is even possible for an already employed individual (salaried worker) to set up a Sole Proprietorship.
What visa do you need?
To establish a business in Japan you will need to hold either permanent residents status (永住者 - Eijusha), long term resident status (定住者 - Teijusha), a "Spouse or Child of Japanese National" visa (配偶者 - Haigusha), a "Spouse or Child of Permanent Resident" visa (永住者の配偶者等 - Eijusha no haigusha tou), or obtain an "Investor / Business Manager" visa (投資家/経営者 - Toshi-keiei).
Detailed information about these visas can be found on the Ministry of Foreign Affairs "MOFA" Website.
You can study the details about laws and regulations concerning the immigration services on Immigration Bureau of Japan Website.
Individuals who start their Sole Proprietorship are required to file a Blue Form called a Kojin Jigyo no Kaihaigyo Todokedesho (個人事業の開廃業等届出書 - "Notification of Commencement of Business") with their local tax office at their Ward / City within 30 days of the business’s establishment.
Do you need a special permit?
Depending on the type of business you decide to establish you will require one or several permits. Since the most common businesses foreign residents decide to establish are restaurants, language schools and export-import trading companies, only permits relating to them are shown below.
Register with the Post Office
If you used your home address as your business address, then inform the post office that mail addressed to your company might be coming. This is a very simple half-page form available at any post office.
Note: if you are living in rented property, it might be necessary to obtain a written consent from the property owner, especially if you have regular visitors.
You will be required to pay income tax (所得税 - Shotoku-zei), sole proprietor tax (個人事業税 - Kojin Jigyo-zei) and residential tax (住民税 - Jumin-zei).
Be sure to keep records of revenues and expenses as well as bills and receipts issued or received in relation to your business. If you decide to set up your own company you will be required to submit an annual tax return to your local tax office.
For more details visit National Tax Agency Japan Website.
Do You Speak Japanese?
Unless your business is a niche business targeting foreigners, a working level understanding of Japanese is vital.
In short, if you don’t speak Japanese, you will always be dependent on someone else, and that is a huge handicap as an entrepreneur.
So why wouldn't you want to use a sole proprietorship?
If you want to share ownership of a business, either with other partners or investors, you need to establish a company.
Another reason is that because the business is not a separate entity, you have unlimited liability - so if your business go bankrupt, is litigated, or something else happens, you are personally liable for it.