Almost all visitors arrive by plane, though some trickle at the border points with Georgia and Iran.

Visas:
Citizens of Australia, Canada, Japan, USA and EU countries can buy a visa when they arrive at any entry point to Armenia. A 21 day visa costs 3,000 dram (about USD8/EUR6).
Visitors from the CIS do not need a visa for up to 90 days. Visitors from other countries must apply for a visa at their nearest embassy/consulate before arriving[2].
For convenience at the Yerevan airport, there is a change booth and ATM before customs and immigration. There is also a hefty surcharge of approximately USD $10 for changing traveler's checks, which in general are not widely used in Armenia. You have to pay the Visa in Dram and can not pay in USD, therefore change at the change booth or ATM before customs.

By plane:
Zvartnots International Airport, 10 km west of Yerevan is by far the main airport in the country.
The national carrier is Armavia, serves destinations across the CIS, Europe and the Middle East. Other West Asian airlines also serve the airport. (Syrian, Caspian[Iran], etc. ). There are very frequent flights from across the CIS. Russian airlines include: Aeroflot, S7, Ural, Polet, Donavia (Rostov-on-Don, Sochi), Kavminvodyavia (Mineralnye Vody), Kuban Airlines, Saravia, Rossiya, Tatarstan, UTAir and Yamal. Others include Belevia (Belarus), Donbassaero (Donetsk, Kiev-Boryspil), Dniproavia (Dnepropetrovsk) and SCAT (Kazakstahn). Several European airlines also serve Yerevan: BMI, airBaltic(low-cost), Czech Airlines, Air France, Austrian, LOT Polish.
Shirak Airport in Gyumri has a few flights from Russia.

By train:
There is a train once a day to Tbilisi, Georgia. The train links with Turkey and Azerbaijan are severed.

By car:
It is possible to drive to Armenia via Iran or Georgia. The borders with Turkey and Azerbaijan are closed. Local travel agents can arrange transport to the border; some Georgian agents can arrange transport all the way through to Tbilisi. Although more expensive than a train or a bus, a private car may be more comfortable and combined with sightseeing along the way.

By bus.

Georgia:
There is minibus (Marshrutka) service from Tbilisi for about $17. Minibus services from Tbilisi to Yerevan take this same route and cost about $35. From this service, it is also possible to get out at Alaverdi (closest major town to Haghpat and Sanahin monasteries).

Iran:
There is daily modern bus service to Yerevan available from Tehran or Tabriz for about $60/$50; check travel agencies for that. Otherwise, the only Iran/Armenia land border at Nuduz/Agarak is very badly served by public transport. On the Armenian side, you can get as far as Meghri by one Marschrutka a day from Yerevan. In both directions, the Marshrutka leaves quite early in the morning. Kapan and Kajaran are more frequently served by marschrutkas, but it is a long and mountainous (and therefore expensive) stretch to the border from there. From Meghri, it is around 8 km to the border and hitching or taking a taxi is the only option. On the Iranian side, the closest public transport can be found around 50 km to the west in Jolfa, so a taxi (around 10-15$) again is the only (commercial) choice. The border is not busy at all, so when hitching, you have to mainly stick with the truck drivers and Russian or Farsi helps a lot here. Consider for yourself whether this is a safe option.