All residents are subject to German income tax for their worldwide income. Depending on the treaties with the countries where the income was earned, you could be eligible for a tax discount, to avoid double taxation. Germany has tax-treaties with most western countries.
When in doubt, ask your realtor to get you an appointment with a tax-advisor.

Tax system
To calculate your income-tax, several income-sources are added.
Per source (for instance income out of employment, rent, business-owner; not: investements) the nett income is calculated (revenues minus costs related to the source of income).
In some cases there is a carry forward service for losses in previous fiscal years.
Deducted are the personal costs such as donations, insurance premiums and alimony.
With this taxable income (Bemessungsgrundlage) the due income tax is calculated:
The first € 8354 are taxfree. After that is starts at a 14% rate up to 42%. 

Investments, capital gains etc
All interests, dividends and (realized) capital gains are charged at 25%.  
Wenn you make a profit (of a loss) in no less then 10 years after the purchase date, on real estate that is not continuously used as your personal home, this will also be taxed at 25%. Renting out your home for a short period of time, could have its consequences, so be carefull.
Be sure to keep all invoices regarding the purchase of the property as well as major improvements, as they reduce your capital gains. Other costs, like maintenance and repairs are likely to reduce your annual income. Your tax consultant knows the details.

If you used your house only as your personal home, you can cash your profit tax free, even if realized within the 10-year period.

If (note: IF) your retirement pension is taxed in Germany, not the full amount is taxed. Refer to your tax advisor for further information.

Renting out
See under "Capital Gains": A profit on a sale of a properties that has been rented out, even if only for a short period of time, will be taxed at 25% (wenn not conducted as an enterprise).
Be advised that the German rent protection is strict and complicated. It will take a lot of money and time to get your tenant evicted.