Assuming you live in the USA, and want an annual income of $30,000USD, after taxes, (if you are single, that should be enough to live frugally as long as the rent is reasonable), you'll need at least $1,000,000USD invested in a mutual fund, averaging 4% anual returns.
This way you'll be protected against an inflation rate of 2% (the current Fed target). Keep in mind I'm not a lawyer, and not American, so I may be underestimating or overestimating the tax burden (I assumed a 20% federal tax on capital income). You can do better in the stock market, with an index fund, but not by a very significant margin.
On the other hand, you could just buy an annuity (for 30k/year). You can probably buy one for 700,000USD, but you'll have a smaller hedge against future inflation (and the taxes are murkier too, I think you'll need a bigger premium just to offset taxes/inflation). So 1 million dollars is still in the ballpark.