The first thing to know about changing trains in Germany is that a train is NOT an aircraft. You do not have to stay seated until the vehicle has come to a complete stop. In fact, you shouldn't.
Keep your eye on the time and the schedule. When you know you are nearing the station, get up, collect you things, and move to the door (usually at the end of the coach). That way you can get off the train as soon as it comes to a stop. If you stay in your seat, new passengers will come into the coach, looking for seats, and you will be like a salmon, swimming upstream, trying to get out.
In preparation for this change, you should know the number of the train you are changing to and the arrival and departure platforms. Since you say there is a 10 minute change in Mannheim, I am assuming it from 12:29 to 12:39 from ICE 690 to RE 1 (4121). According to the trip details on the Bahn website, the blue boxes to the right of the time of change, you will arrive on platform 2 and depart on platform 1. Mannheim is a typical Bahn straight through station, where platform 1 is next to the station building, tracks 1 and 2 are next to each other in the gap, and platforms 2 & 3 are on the next platform. To get from platform 2 to platform 1, you will have to go down stairs into the cross tunnel, find the sign for 1, and go back up the stairs to your platform. If you keep moving and walk normally, it shouldn't take 10 minutes.
When you get off the train, you might see signs with white and yellow sheets behind glass. These are the schedules of trains in and out of that station. The white schedules are for trains arriving. Forget that, you're already there. The yellow sheets are for departures. The sheet is organized by hours and destinations.
Find the time of departure and the destination (or the train number). The sheet will show you the platform and the time. These sheets are printed months in advance and don't change. Make sure the platform number agrees with what you already think it should be. Then proceed to that platform.
When you get to the platform, there will be an overhead lighted sign with the train number and the time of arrival of the next train. If you are very early, the train shown might be the next train, not yours.