Here is a short description of the Covid PCR Test I did in the middle of December 2020. This was for travel purposes which you have to pay for yourself.
I registered online at Centogene Frankfurt Airport. The Test Centre is on the bridge as you walk from the Long distance trains to the Terminals. You can also select a test centre airside in the Transit Terminal. I selected the Premium 24 hours test, and added the €9 Identity verification. You will have to upload a copy of your passport.
You cannot make an appointment, you just pitch up with your documentation. You must bring your test confirmation papers with the QR codes on, as well as your identification documents like your passport. Do not eat or drink anything 15 minutes prior to your test.
After checking your documentation you are redirected to a queue. When you get to the front of the queue they ask for your printout. You then wait to be called
Next you will go to the testing booth. They use a swab in your mouth and throat, but do not collect material from your nose cavities. They take two samples.
When finished, you report to the desk where your identification will be verified.
The results will be sent to you via an Email with a link. You can then log into your account and download your report. You can choose to print the report in English
The report shows the date and time of the test, as well as that of the results.
I went on a Sunday really early (arrived just after 07:00) and there were no queues, we waited max 15 minutes to be tested. We received our results the same day, after about 5 hours. The report was available to print or save as a pdf. Other people waited longer it really depends on the time of day.