Visitors to Yerevan have couple of options to go around the city using public transportation. There are some buses and minivans (locals call these Marshutkas), which will take you about anywhere in Yerevan and cost only 100 AMD.
There is also an underground subway, but does not have a lot of stations. The ticket for it also costs 100 AMD and you can get it at every station. As an alternative you can always take taxis, which you can find anywhere in the city or just use Uber-like Armenian service called GG. Going around the city center by taxi will cost you 1000 on average.