It's quite simpel. And when you use the *A book and fly tool it will automatically check if your chosen route complies with the rules.

A regular *A RTW allows you a maximum 15 of stopovers. That's a destination where you plan to stay for more than 24hours. If you have another flight planned that leaves within 24hours of your planned arrival it's considered a transfer.

So just determine the places where you want to go (and stay longer that 24hours). Those are your stopovers. You can visit multiple cities in each country (max 3 in a country / 5 in the US). You just have to be aware that when you use non-direct flights, sometimes a transfer somewhere along the route is needed, the total of stopovers and transfers cannot exceed the maximum of 15.

But in reality just consider the places you want to visit. And determine if there is a direct flight available. If no direct flights are available each transfer will be one less stopover/destination you will be able to make.

But unless you ha a long time in which to complete your RTW it's probably not a really good idea to start with 15 destinations ;-)

And the *A website is, in my opinion, the best source of your information. Most airlines don't have a decent description of the RTW terms and conditions.
Just use the book and fly tool on the *A website to make up a dummy routing and choose the available flights. In the tool you will see exactly how many stopovers and transfers are needed, and even what the pricing and taxes will be. Your routing will be checked against all conditions and you will get a decent overview which flights will be available between cities.

You can even use the book and fly tool to make your final reservation (or use a travel agent). Availability for the dates and flights you will need is checked when completing your route and when you make the booking confirmation is instant. You just need a credit card :-).