You are permitted 16 segments, which means 16 times you can travel from one airport to another, either by flight or by surface. Each flight code uses a segment. So, if you fly QF2 LHR-SYD, it is one segment although it's a direct flight in two parts, LHR-SIN and SIN-SYD. However, if you want to go from ANC to CUR and fly AA148 ANC-DFW, AA2386 DFW-MIA, AA2739MIA-CUR that uses three segments.

What I do when planning an RTW is pick the places I want to stop, and use ExpertFlyer to see the available flights between them. I like EF because it shows if the flight has the right inventory (e.g., A, D, L), what type of plane, seating, timing, etc. It can search a week at a time, which is handy because some flights only operate certain days.