There are several guidelines written by travelling bloggers already – thank you for all those (e.g. Backroad Vagrants)! We experienced a slight change in the procedure since, so make sure to read this update (End of 10/2018, information without guarantee):

1. Get a E-Visa-reference number

Contact an agency, we heard it is more successful (e.g. key2persia).
Fill the form with your trip scedule.
Send a copy of your passport and a passport photo (women do not necessarily need a head scarf on the photo – at least it was working when I applied) via Email to the agency.
Pay 35 $ via Paypal.
If you like, make sure the embassy received the E-Visa-reference number by calling them.

We got our forms after 2 days already: first contact to the agency on a Monday, E-Visa received on Wednesday. Working days in Iran: Saturday – Wednesday.

2. Visit the Iranian embassy in Yerevan

Opening hours for visa matters: 2 – 4 pm Monday, Wednesday, Friday.
We warmly recommend you to be at the embassy at 2 pm due to the following procedure:
Once inside, pull a waiting number. At the desk, you will hand your passport for checking and afterwards, you are required to go by taxi to the Mellat Bank to pay the visa fee (https://goo.gl/maps/yvivPw7K1192). It takes you 20 – 30 min depending on traffic, costs 800 Dram (Yandex) – 1200 Dram (ordinary Taxi).
Pay 50 Euro cash whatever currency at the Mellat Bank for the Iranian Visa (this ist he price for an ordinary prodeeding time for European citizans). There is no ATM at this bank, just next door. Go back to the embassy untill 4 pm the same day, hand them your passport and the payment confirmation from the bank. The embassy keeps your passport, you will get a paper instead and will be told to come back to receive your visa.

We went on a Monday, visa were ready on Wednesday. If you pay 75 Euro, you get the Visa the same day.
If you are hungry afterwards, there is an Armenian cafe Nor Tonratun on the other side of the park at Komitas Ave.

3. Visit the embassy again to pick up the Visa

This time, you do not need to pull a waiting number: show the guard at the entrance your pick-up-receipt and you will quickly get your passports with visa at the desk.

Unlike the other bloggers mentioned, the procedure at the embassy did NOT require to have printed the following documents (at the time when we applied):
– travel health insurance
– passport photos (with headscarf)
– copy of passport
If you anyway need to print sth. or take passphotos, go to the big supermarket Yerevan City close to the embassy on Komitas Ave. In the basement, there is a photographers shop, cheap prices.
Enjoy Yerevan and happy travels!