I found the *A RTW site to be a good start for planning my itinerary and estimating costs. For the booking itself, I wrote my itinerary and options down in an email for SQ and then called them. They will take some time to book and quality of agents vary greatly (some have never booked a RTW for eg) and I imagine this is the same for other partners. So tell them exact flights and times, and book early to ensure availability. There are also many itinerary rules you need to be aware of, so read the RTW TnC doc first:

https://www.staralliance.com/en/round-the-world?view=tc