I remember at first it was kind of confusing. I did not grow up using public transportation at all. But, once you get used to it, it is easy to read the schedules and find connections. You think in your head, "We only have five minutes to change trains...no way!?" but it always works.
Here is the lowdown on how it works:
DeutschBahn has these kiosks at all the train stations in Germany. They often are in English, though you do need to know the German name of the town you are going to. You can look up connections from anywhere to anywhere. Not only can you buy tickets through the kiosk, but you can type in your destination, the date and approximate time you want to go, and they list all your options, plus or minus about two hours of your intended time of departure. You can easily scroll through to change times as well.
So, for example, you want to connect from Freiberg to Berlin, on Tuesday about 9AM. You put that information in, and you see that at 7AM there is a direct ICE train, taking 3 hours, no connections. At 7:30 there are regional trains, with numbers and connections and they list what track they leave from and what time you arrive and depart at the connection stations. This trip option takes 4 hours. At 8AM there is an ICE with one connection, taking 3.5 hours. And it goes on until about 10AM. If none of the options sound good, you switch times and look again.
Now here is the cool part: you can print these out from the kiosk, so you can either print out several and think about it, or just print the one you buy, so you don't have to write down your times and connections. Like I said, they also tell you what platform you disembark from, and have to get to in the time between trains.
Most countries have a variation of this system, but again, you need to know the names of towns in the local language. For instance, in Italy, Florence is really Firenza.
If you are on the road and just want to look ahead to see what connections are available, there is also a DeutschBahn app you can pick up, which tells you train schedules and connections all through Europe. The link is to the iPhone app, there is an android version also.
The other option is to go up to the ticket window and buy direct from the agents, who are very helpful; more helpful if you can greet them in German first, but then they are happy to switch to English as needed.
You can check out your train options ahead of time by looking at the schedules posted on the platforms and walls at the station; departures in yellow, arrivals in white, with in-between stops and times all noted.
At some of the platforms they have a diagram that shows the various trains that use that platform, and which cars are which. So, for instance, if you have a second class, unreserved ticket on the 5:14 ICE train, the diagram shows that on platform #2, if you stand under section signs A, B and C you load up on the first class cars. The dining car is at section D, second class loads on section E back to G and then the baggage/freight car is last.
See the "Train" photos below, and this all makes sense. I did not set these photos up to run automatically as a slide show, so you can look through them slowly and study the photos.
We learned this all from spending time waiting at the stations, experimenting, looking at the signs, talking to people, and figuring it out through desperation!