How do you become an accredited investor?
By meeting one of the SEC's tests: income over $200,000 ($300,000 with a spouse or partner) in each of the last two years, a net worth over $1 million not counting your home, or holding a Series 7, 65 or 82 license.
There's no application or registration. You qualify or you don't, and the fund decides whether you do. Many funds take your word for it in a questionnaire; offerings that advertise publicly must check, usually with tax returns, account statements, or a letter from a CPA, lawyer or broker.
The license route is the only one that doesn't depend on wealth: passing the Series 65 exam, for example, qualifies you while the license stays in good standing.