Can I find a job in Germany as a Graphic/Web designer?

[Tarostar]

I heard there is shortage of people in the field of media.
Is that true? And how hard is it for a non-Eu citizen to find a job in Germany?

[Lou]

you will need to call THEIR employment office to have that question answered

[Josie]

There's a shortage in the field of IT (information technology), so if you have qualifications as a system administrator, programmer or anything like that you might be lucky.

The Arbeitsamt has a search engine on their page.
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Click on "Jobbörse" and a search form will open.
In the field "Beruf / Tätigkeit / Ausbildung" enter the search term "Web-Designer/in", then click "Suche ausführen".
You can also adjust the search criteria by defining a city or area around that city, if you already have an idea where you want to live.

Also, speaking German is definitely an advantage to get a job.

Generally, it's pretty hard to get a working permit if you're not from the EU. It's a little bit easier if you have a contract with a German company.
I'd recommend you contact your local German embassy. They can provide you with the neccessary information and help you with the paperwork.