First off, a quick correction to terminology-- it's better to say most people will be living off the returns of their investments, since interest is just one type of way to make money on investments.
Second, there are as many ways to live off the returns of your investments as there are investment strategies. I'll cover a few, but there are probably hundreds of ways to make this work. These are just a couple common ones used by many people here, and most of us use a combination of at least a few of them.
1) Returns from taxable accounts. You hold investments in an after-tax account. This means you get paid by your employer and the employer takes out taxes, and then you invest the money. You fund your retirement either from dividends (payments made to shareholders to share profites), gains (when you cash out the asset after it has gained in value) or both.
2) Returns from tax-deferred investments. You defer part of your salary into something like a 401(k) and don't pay taxes on initial investment. When it comes time to retire, you can cash out a small amount of the investment periodically, paying taxes on withdrawal. If you are of the retirement age, you can do this without penalty. If you retire early, there are various strategies to "pipeline" this money out to avoid early withdrawal penalties. The most frequently used methods of doing so are the Roth IRA pipeline and SEPP. You can Google both these terms or search this forum.
3) Returns from Roth IRA accounts. The Roth IRA is also an investment account. It is funded with after-tax dollars, but grows tax-free. Again, when you need to fund your retirement, you simply cash out whatever portion of the investment you need at whatever interval you want.
4) Cash flow from real estate. Many people prefer to own real estate and grow an alternative income stream through rents. So you would invest in real estate, place tenants in that real estate, and the remainder of the rent each month after mortgage, repairs, property management, and other costs is cash flow. Once you have enough to replace your income, or whatever amount of income you need in retirement, you are financially independent.
These are just a couple common examples. There are so, so, SO many ways to retire early, and each person has their own strategy and comfort zone. The above are just the most commonly seen.
My personal strategy is a combination of real estate, tax deferred investment, and taxable investments. Specifically, I am building cash flow in real estate to replace about 50% of my expected costs of retirement. I am maxing out my 401(k), and putting everything left over in taxable accounts. On retirement, I will fund the first five years with Real Estate cash flow and my taxable accounts, while filling the 5 year Roth IRA pipeline from my 401(k). Once the pipeline is full, I can stop using the taxable account and save it for emergencies.
