You need to have "intellectual property" of some sort (patents, brands for franchising, copyrighted software). You create a number of corporations - one that is tax resident in a tax haven like the Cayman Islands and domiciled in Ireland, one that is tax resident in Ireland, one in the Netherlands, and one in each country where you sell your goods or services.
You then go and hire a good tax accountant who has experience with the Double Irish tax dodge (look it up on Wikipedia), and Bob's your uncle. (Though a double irish is harder to create for new firms since 2015 - you might have to acquire a ready-made shell corporation.)
Of course all this only makes sense if you have profits in the tens or hundreds of millions, so that paying for the shell companies, your Irish headquarters, your tax accountants and your lawyers is cheaper than actually paying tax.
The part I don't understand is that the brand was developed in the US. Don't you have to transfer the IP at something approaching fair market value to the tax haven corporation? How could you possibly have the resources (in the haven, no less) to do this without loaning money (at interest?) backwards?
So if you sell something on the open market anywhere, you can't sell it to your foreign subsidiary or owner for too much more or less than the open market price. But things get dicey when you're talking IP: patents and trademarks don't trade on the open market but are absolutely vital for a subsidiary to be alive, right? Amazon isn't Amazon if it can't call itself "Amazon".
The other trick is to offer some kind of service that's difficult to precisely quantify like having an accounting or service center in one country that every foreign subsidiary is required to pay for. It might not be a reasonable price but the cost of auditing all the call center records to find out it's costing $3/minute (on average) for a particular US based company to outsource its support calls to somewhere instead of $0.10/minute is going to be very steep. Do this across a few different lines of corporate support and your profit hiding is accomplished.
You then go and hire a good tax accountant who has experience with the Double Irish tax dodge (look it up on Wikipedia), and Bob's your uncle. (Though a double irish is harder to create for new firms since 2015 - you might have to acquire a ready-made shell corporation.)
Of course all this only makes sense if you have profits in the tens or hundreds of millions, so that paying for the shell companies, your Irish headquarters, your tax accountants and your lawyers is cheaper than actually paying tax.