Getting a German work visa/permit without a job offer is virtually impossible. But it's indeed easier for a selected number of fields including IT as a job offer is all you need in this case. In other fields, you need to have a salary above a certain threshold and to prove that it's not possible to hire someone locally (Arbeitsmarktprüfung or “job market examination”), which means your employer should submit a lot of information to the authorities and wait several weeks to see if other people apply.
Because jobs in IT are exempt from these requirements, I don't think the employer has to send an “invitation” or go through any other special paperwork. All a prospective employer needs to do is extend an offer and provide a job description and you, the employee, could take it from there and apply to the consulate yourself. It's supposed to be relatively quick as well.
Having a degree from a German higher education institution is another way to be exempted from this “job market examination” and salary requirement. It would also give you the right to stay in Germany to search for work at the end of your studies. So if you can't find a job right now but are still a student and really want to immigrate to Germany, it could be an interesting route.
If you qualify (annual salary over EUR 37000, again only for IT and other technical fields, EUR 47000 otherwise), you could also apply for a EU blue card. The main advantage is that it should then be easier to move to another EU country while still building up permanent residency rights.
More information on all this can be found on the site of the German Ministry for Foreign Affairs and on Wikipedia (both in German).
Note that legally speaking you cannot work at all (not even for a month or two) on your Italian residence permit, at least not without separate authorization from the German authorities. As an Iranian citizen, you also need to go back to a country where you are a resident to apply for a long-stay visa for Germany, you can't do it from within the country on a short-stay visa (or visit with your Italian permit).