How do Institutional Investors buy/Sell large positions without causing huge market impact?

If an institutional investor wanted to buy/sell a large chunk of a company without slippage, what methods do they use?

I read an article about dark pools but didn't understand it completely.

Are prices set by order books or by the NBBO?

If by NBBO, is there a limit to how many shares they could reasonably sell?

For example if they owned for some reason 20% of a company, could they realistically get this through 1 block trade at the NBBO if a Dark Pool was used?

If not, is there a way to estimate how many days a trade would take based on average volume of the stock or position size maybe?