Check that you have all your belongings
Go into the main area of the station (unless you're already standing in front of your next train)
Find a very large screen displaying all departing trains
Check how far into the future they are displayed. If it cuts off before your planned departure, you'll need to wait a bit before your train appears on the screen.
Once you recognize your train in the list (by name and final destination), check what platform is listed for it. This might be different than it says on your ticket, because they sometimes change it. Remember the platform number that is displayed on the big screen!
Go to that platform number. There are numbered signs in the big hallway that connects the platforms. Long platforms also tell you a letter after the number, which means a specific position along the length of the platform.
Once you're at the platform, check the screen on the platform (if it is working). It tells you what the next train is. It might be your train, or it might be another train that's arriving before it. It's good to keep track of them so you know which one is yours.
While waiting for your train, listen to announcements. The train might be delayed or moved to a different platform or cancelled. This will be announced on the speaker and on the screens on the platform.
If you're going on a train that splits into multiple parts, prepare yourself to go on the correct part. There is hopefully a diagram on the screen to show which part of the platform is correct for you. It might also make sense to ask other people, because splitting trains are tricky as a beginner. Moving between these train parts is not possible through the train's interior. If you entered the wrong one, you'll need to step outside and back in.
This is the first stop. The train will arrive well in advance. If there's already a train on the platform, check if it is yours. Usually they already allow passengers to enter long before departure.
The screens on the side of the train and inside the train might be displaying your correct destination, or they might still be displaying data from its previous trip. Depends on how pedantic your driver is on user experience.
In a confusing situation you should ask a conductor for help. They know how difficult train travel is to beginners because they see it all the time, and will gladly help you.
Remember the name (number) and destination of your train.
As the train is arriving, you will see small screens or papers on the side of the train, they mention the name/number, destination, and a few inbetween stops. Double-check the destination and name of the train (your ticket is bound to it).
If it is not matching what you expected, then this is the wrong train or the screens are displaying the wrong data (this happens rarely). In this case, immediately ask a conductor "is this train to <your destination>?"
The train typically stops only for a minute and you need to decide whether or not to get on
If you have less than 10 minutes, there may not be time for all of above. In those cases, you need to already know what to do in advance. If it's a short connection between two trains, you should ask a conductor while you are still on the previous train.
In Germany, you can use the website bahn.expert to see information on departing trains. The same information that you would find on the big screen in the station.