How do custom officers determine if the imported goods of a passenger are old or newly bought?

To add the other answers (the one by Relaxed is spot-on - customs officers use their intuition), here comes some information about the legal situation, adapted to your case (Germany). Note that IANAL - so this is information is all only to the best of my knowledge.

Legally, it is enough for the German Customs officers to suspect that something is imported to the country for the first time. There is no legal necessity for them to prove it before they can ask you to pay customs (and a fine for undeclared goods). Of course, in obvious cases of wrong decisions by them, your chances to appeal are quite good. But in principle, it is the reponsibility of the traveler to provide a proof that the goods you bring into the country have been brought back by you. This is particularly relevant in case of electronics.

There are two ways to do so - either you carry a receipt for the good with you that lists a serial number and that thus proves that the good has been bought within the EU, or (2) before you depart from Germany, you go to your local customs office with the goods and have them prepare a form for "good re-entry" for you. The official term for this is "Nämlichkeitsbescheinigung" (which is probably the most uninformative term ever invented - it roughly translates to "Proof of Particularity", which means nothing - just as the German term). Typically, your goods will need to have a serial number for that approach to work.

I don't think you will find a concise answer and even if there was one, Customs & Immigration Departments would not want it known publicly. In very generic terms ... They Observe. They are trained to read your body language, to interpret the way you answer, to go beyond the surface. They look at how you dress, what you have, where you were, how long you were there, why you were there. And then they make judgement calls based on what they have observed.

While they have set examples they use in training, it is mostly time on the job that improves their judgement. Perhaps the customs agent you had a hard time convincing was new on the job or maybe was just having an off day.

In some cases the custom officers can see if something is bought on your trip or brought by you from home, by looking at the serial number. Quite some electronic devises keep a log of serial numbers, country where it was sold, etc.

However in most cases, it all is very subjective and probably dependent on personal decision by custom officers. The only thing, in my opinion, you can do to prevent this is to keep proof of purchase of the goods.

I do this by storing scans in dropbox and always have access to my dropbox from my devices (tablet/smartphone). Since you will probably not bring that many brand new devices you could also choose to simply carry a copy of your receipts with you.