You buy a publicly traded REIT exactly the way you'd buy a share of any listed company. Open a brokerage account, search the ticker, place an order. No application, no approval, no accreditation requirement. Accreditation, which is a set of income or net worth thresholds under securities rules, applies to private offerings, and that's likely what you're thinking of. Private REITs and non-traded REITs are a different product with different rules, and the term REIT gets used loosely for all of them, so be precise about which one someone means when they say it.
The realistic minimum is the price of one share, and many brokerages support fractional shares, so a few hundred dollars gets you started. There's no separate account minimum at most large brokerages and no commission on stock and ETF trades at the big ones. If you go through a fund you'll pay an expense ratio, often somewhere between 0.08 and 0.5 percent a year depending on the fund, taken from the fund's assets rather than billed to you.
The piece that matters for someone coming from land is the income timing. A REIT must distribute most of its taxable income, so you'll get dividends quarterly, typically in the 4 to 6 percent range for the sector. Those dividends are largely nonqualified, generally taxed as ordinary income, which is why many investors hold them in a tax-advantaged account. Land taxed on eventual sale and REIT income taxed annually are very different problems. A tax professional can tell you what that does to your specific situation.