In order to play, one person chooses a city. Every city after must start with the last letter of the previous city. You must prefix every city with ! for it to count. You can also specify regions and countries by separating them with a commas after the city. 
For example, a game could look like this: 
Person 1: !london
Person 2: !new york city
Person 1: !yerevan

!london and !london, uk would both count as London, United Kingdom but you could also do !london, canada, or !london, ontario to specify London, Ontario, Canada

Voting for Cities Chain