I don't actually think "how" is even a question at this point. If you poke around wikipedia's (clearly incomplete) list of cooperatives and employee-owned* companies the answer is/has-always-been pretty clearly: just like any other form of company works.
*coops however aren't necessarily employee owned-- there's a several models-- and ESOP style employee ownership can be pretty weak from an ownership perspective so in addition to being woefully incomplete the lists should also not be taken at face value.
A lot of large infrastructure projects, for example, are funded by loans with very little (or none) equity capital. Risk is borne by the firm, its lenders, or the state. The "owners" are basically they guys who get the deals made.
I have no idea if employee-owned companies will be any good. There were examples (eg Egged) in the past that didn't work well. But it's curious to see them taken as an impossibility for reasons like this, that they don't fit inside of a textbook free market example, with all incentives perfectly aligned. Half the companies in the world weren't started this way. How did Russian oligarchs buy all those state companies? Leveraged buyouts. IE, the banks (does this count as the state?) gave them money to buy (or start) them.
The more interesting questions are around management. How does an employee owned company work well? Answer that with confidence, and I think everything else is solvable.