Public transportation is very good and inexpensive in Armenia. The following types of public transportation are available in Armenia: metro, bus, minibus, taxi, etc.
Metro: Yerevan subway system has one line stretching from the north to the Railroad Station in the southern edge of the city. There are 10 stations. The fare is 100 AMD (0.2 Euro / 0.25 USD) per ride.
Bus routes cross the city in major directions but it can be tough to get to more remote sites outside of populated areas. The fare is 100 AMD per ride. Minibus routes, these 12/16 seat small busses connect virtually every point to every other point in the city. The fare per ride is 100 AMD. They run until late night.
Taxi Service: Probably this is the most inexpensive taxi system in the world. Average ride costs 1000-1200 AMD (2-2.4 Euro / 2.5-3 USD) per ride within the central part of the city, not including the tip! You can find plenty of taxis in the city, from well-loved Ladas to late-model Benzes. Trains in Armenia are Soviet-style and a little slow as a means of moving around the country. Trains can be taken up to Gyumri and from there on to Alaverdi and Georgia, or they can be taken up to Lake Sevan all the way to the far side.
Plane: Domestic flights are not an option as there are only two working airports and no internal flights in this small country. Intermittent service to Karabakh has been available in the past and scheduled flights from Yerevan to Stepanakert may start up again - if passengers can be assured that Azerbaijan will not shoot them down.
Note that unlike many countries in Eastern Europe, Armenian minibuses and buses do not sell tickets beforehand and, in fact, do not issue tickets at all. You simply pay the driver at any point during the trip (though some will collect at the beginning). Exact change is never required, but a 20,000 note for a 1,000 dram ride might present a problem. Tips are unheard of on public transportation except taxis.