Depending on what places you visit and what you’re planning to do there, the need for public transport and transport availability will vary. In central Yerevan, you might not need public transport at all. In case you do, there are buses and mini buses (you can find the routes on Yandex map) as well as the Metro (one line).
Nevertheless, the main transportation means in Armenia is the taxi. It is affordable in Armenia, and if you want so, you can even take a taxi to a different city. There is a variety of taxi services, some of them operating online, such as local GG Taxi service.