Many of the cantons have economic promotion / business development offices, which advise people wishing to start a business.
For example, in the Basel region, the office is the BaselArea Economic Promotion Office (
www.baselarea.ch). They provide advice and assistance free of charge.
Generally speaking, anyone can start a business (e.g. a limited liability company needing CHF 20,000 capital) as long as there is at least one resident person, who can sign on behalf of the company. The rules for becoming self-employed are a bit less straightforward (normally must be an EU/EFTA citizen or hold a C-Permit, although there are exceptions).
Good luck!