How did the Germans know who the Jews were during the holocaust? Was it a characteristic like eye color or something? Or did they just guess?

No, the German authorities could hardly see a difference between Jews and other people.
The German Jews just looked like any other people and there were many of them who looked much more arian that real Germans.
Up to the time of Hitler they were citizens as anybody else and many had very reasonable and responsible jobs and positions and many of them risked their lives in WW I. The Jews were absolutely loyal to their country.

But in Germany since ever and even up to now there is existing a resident's registration office in each town and each village and if people are born this is noticed at the registry office which is also in each village and city.
Everybody is obliged to tell the registration if you move away and when you arrive you have to register also.
In the registers there is always noted the name of the parents, their nationality and the religion because people have to pay tax for the churches which are collected by the government.

So for the Nazis, who were first of all overtaking full command of the police just had to investigate all registers in each village and each town.
So they found out who was a Jew or not.
And finally after a few years everybody who wanted to have a job in the public service or a leading position in economy had to bring a family tree of at least 3 generations. If this family tree was obscure, many Germans lost their jobs even if they were in high positions.
Of course it was an extreme administrative duty, the Nazis had enough people who did that job.

Within Germany, the Nazi's required everyone to prove their genealogy by showing their family back 3-4 generations. This was in the mid 1930s, before they started rounding up jews. If you had any Jewish ancestors, your identity documents were marked.

SO, when the Germans started to increase persecution of the jews (making them wear start, prohibiting them from many activities, etc.), they already had pretty good records of who the jews were.

When the Nazi's started invading other countries, they found that the jews inmany countries were already being tracked. For example, in the Soviet union, everyone had identity papers that listed their nationality (ukranian, etc.). Jews were listed not as just a nationality, but as "Jew". This made it very easy for the nazi's to hunt down Jews in occupied areas.

Is this a real question, or just an attempt to stir up controversy?

There isn't any secret about the fact that they required Jews to sew stars on their clothing long before they made their intentions known. Once they were all suitably marked, it made it really easy to single them out and move them into closed, fenced off ghettos. And once they were in the ghettos, they just came in and rounded them up when they wanted to.

I think surname had something to do with it as well as the fact that most were business owners (made it easy to see who closed up for Sabbath) Mezuzah's by the front door, Menorah in the window for all to see, plus obvious signs and symbols (Star of David and things like prayer shawls worn like aprons by males). I don't think so much hair, skin, eyes etc...so much but I could be wrong? I am blonde with blue eyes. I think surname if I had to just choose one.

This is the main site
http://fcit.coedu.usf.edu/holocaust/timeline/timeline.htm

This relates to yout question
http://fcit.coedu.usf.edu/holocaust/timeline/ghettos.htm

The Nazi's did utilize Eugenics, a bogus science that studies the differences between groups of peoples, to justify their beliefs, however, as this was a bogus science it really couldn't be used to determine who was Jewish or not. During the time period your religion was something was known about you and your family. On top of that groups usually lived together, not to say there wasn't a bit of integration but the minority groups tended to stick together. Differences most of us hardly notice today decided where you lived, shopped, went to school and who you associated with.

Hair, facial structure, and skin colour.