1. PE company secures a loan in the company’s name (usually contingent on a turnaround plan executed by the PE with a history of turning companies around)
2. Company turns around and loans the money for purchase to PE firm
3. PE firm buys the company
4. PE firm runs the company, normally collecting management fees (paid out of the pool of cash used to buy the company)
5. PE firm cashes out by IPOing the company (usually at the same or higher price paid during LBO process).
6. PE firm uses the proceeds from the IPO (which the PE keeps because they are the sole shareholders; NOT the company itself) to pay back the loan.
The PE usually breaks even on the transaction itself once transaction fees are taken into account; but they make a killing on the management fees (which can be hundreds of millions a year). Normally, the company is left in roughly the same situation as before the buyout, just with a lot more debt on the balance sheet.