Unless you hold a passport from a European Union member state, you may not work during your stay in Germany, except at the university and except for the 120 days (or 240 half-days) of work included in a one-year visa. If you have a visa in your passport (which everyone should have) you are allowed to work 120 days per year. Therefore, you may work outside the university during the lecture-free period (vorlesungsfreie Zeit) or work part-time during the semester, depending on how much time you have. If you want to work for longer than 120 days, you will have to contact the Ausländerbehörde (foreigner's office) to get permission and the respective changes to your visa. If you work without a permit in your passport, you could be reported to the police.
Only relevant for students on internship semesters
You will have to obtain your "Lohnsteuerkarte" (income tax card) from the registration office (Einwohnermeldeamt). You will need this card if you stay in Germany for more than six months. Submit this card to your employer when you begin work. You will get this card back at the end of your internship semester for the „Lohnsteuerjahresausgleich" (tax rebate). Inform the company where they should send the card to.
If you work for less than six months in Germany, you will not receive an income tax card. In this case, be sure to remind your employer to ask the relevant tax office for a "Bescheinigung für beschränkt steuerpflichtige ausländische Arbeitnehmer" (certificate for foreign employees who do not need to pay the full tax rate). Otherwise, the full tax will be taken from your income and you will not be able to claim a rebate.
With a tax card, you can claim back some of the tax you have paid. Forms can be obtained at the reception of the "Finanzamt Karlsruhe-Stadt" (tax office), Schlossplatz 14, Karlsruhe. Try to keep all of your receipts (train, flight, and tram tickets etc.) and hand them in, together with your application for a tax rebate, to the tax office. This should be done before you leave Germany. Note: the tax office does not transfer money to banks abroad.
Finding a job after graduation
The Ministry for Science, Research and the Arts of Baden-Württemberg notifies:
Foreign students, who are not nationals of an EU member state, are permitted to look for a job in Germany for a period of one year. If they do find employment, they will be given a residence permit restricted to this employment. After two years' employment or three years' residence they will be entitled to a work permit without being restricted to a specific company.
Persons from Eastern European EU-member states who completed their degree at a German university will receive an EU-work permit initially limited to a period of one year. After one year's admission to the German labor market they will be entitled to receive an EU-work permit. This permit is issued without restrictions. As they do not require a residence permit, the question of restrictions on residence is not an issue.