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This achievement is as straightforward as its description states. You simply need to have one caravan to each of the following five civs at the same time (note that they must be land routes, trade ships do not count towards this achievement):
Harun al-Rashid (Arabia)
Wu Zetian (China)
Gandhi (India)
Genghis Khan (The Mongols)
Darius I (Persia)

I recommend the following start:
Age: Renaissance or later (Banking is needed for your 5th trade route unless you have the Colossus and/or Petra)
Map: Pangaea or similar one-continent map (trade ships don't count so if there is no land route between your civs you'll have to found a city on their land mass).
Map size: No bigger than Small (so it's less likely you'll have to found a bunch of spread-out cities)
No barbarians (so they can't plunder your trade routes)
Policies: Liberty -> Republic -> Collective Rule (in case you need a third city to reach all of the civs)

Found your first city and explore around you as much as possible. Once you've found all the other civs found your second (and possibly third) city as close to as many of the others as possible. Trade routes have an initial range of 10, boosted to 15 with a Caravansary so keep that in mind while choosing your city locations. Build a Caravansary if needed and then churn out your 5 caravans. Once all of the civs are connected the achievement will unlock!