I do an around the world about three times a year. You do it by airline alliances (Star Alliance or one world). If you are in the USA the fares for C are about $6,000.00 plus taxes. For F it is about $7,400.00. A suggestion: I use Star Alliance. To start in USA is most expensive. Start in Canada and use Air Canada and Star Alliance. C is about $4,200.00 and F is about $6,200.00. Often starting in other countries ( if u live outside USA is cheaper. South Africa and Australia are good. Best is Malaysia.) You can save alot by not starting in USA.
There are levels of miles traveled. For the above you must stay under 29,000 miles, head in the same direction, be gone 10 days and make 3 international stops. The more miles over 29,000 u take the higher the fare. You call the airlines you will use first and they make the arrangements.
If I were to fly from the USA to South Africa in C, it would be US$ 7,500.00 rt. I can do an around the wolrd (go on to Singapore and Australia) in F for the same amont.
There are "bucket shops" in London which can offer good deals.
Hope this helps.