If I am living in Germany (I am not a German citizen), and travel to Turkey for a single day, and come back the next day (it is the earliest flight back to Germany), do I need to go into quarantine for 14 days?
Traveling to Turkey
According to the US Embassy in Turkey:
COVID-19 control measures for air, land, and sea travel continue. Passengers arriving in Turkey will be required to complete an information form and will be checked for symptoms. Anyone suspected of having COVID-19 will be transported to a hospital for examination. If an individual on a particular aircraft/vehicle/vessel is found to have COVID-19, the information forms completed upon arrival will be used to identify others have been in contact with them; those individuals will then be subject to 14-day isolation/quarantine.
So unless you're suspected of having COVID-19 and test positive, you will not have to quarantine, at least as of July 27th 2020. However things change rapidly as the pandemic progresses so please check the above page a few hours before you travel just to be sure.
Coming back to Germany
By default, you will need to undergo quarantine:
In principle, travellers entering Germany from the United States must spend 14 days in home quarantine immediately upon Arrival. Upon entry into Germany following a stay in a risk area within the last 14 days.
However you can skip the quarantine by getting a negative PCR test in advance in Turkey or after arrival in Germany:
If you can prove that you are not infected with the SARS CoV-2 virus, these quarantine regulations do not apply. This proof must take the form of a medical certificate. The molecular test to detect an infection must have been conducted no more than 48 hours prior to entry (i.e. the swab must have been taken no more than 48 hours prior to entry). The test must have been carried out in a European Union member state or a state with comparable quality standards. Alternatively, the test may be carried out upon entry at the border crossing point or at the place where you are staying.
And Turkey is indeed on the list of states with "comparable quality standards".