Travelling from Germany to Iran

Given the fact that you have only one week at your disposal, I would recommend flying. Your best bet is to be flexible on the travel dates and to monitor possible special offers. With this in mind, check out Pegasus Airlines. At the time being, they have interesting fares for destinations in the Middle East (via Istanbul Sabiha Gökcen). As an example, for May 2012, I found a Düsseldorf-Tehran return ticket for less than 300 EUR.

You can take a round-trip flight from Istanbul to Tehran around $300 (at the best case $200). Of course you cannot find a cheap flight for a one-way trip. I recommend a direct flight from Berlin which will cost about $500.

And no, you do not need to learn the local language for this trip. English is enough!

Traveling

I guess the cheapest option (and more adventurous) was already mentioned by RoflcoptrException.

However, it does not feel like the recommended version nowadays, mostly due to the war in this. If someone stumble upon this page and also consider to pay a bit more (and gain more comfort), I would consider flying.

Flying to Iran recently becomes much more convenient compared to 2010-2012, were the only option was Turkish Airways (stopover Istanbul) with an arrival time around 3am at Tehran. Since last year, there are also direct flights offered from Berlin to Tehran by Germania lasting around 5 hours for ~400€ (return, 2016). Flights are Tuesday/Saturday and scheduled overnight, so one can maximize duration of stay at Iran.

Language

You do not necessarily find to many people speaking English in Iran. This is particularly bad when you have troubles with your luggage or ticketing etc. However, there is always some way to solve issues, most likely, they will try to find someone who is able to help out with English/German/etc..