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Why methods tooevoegen() and remove() are not implemented? Their implementation must be one trivial line of code, if you look at the List API.
Also, it would be nice to override toString method in...

In your main method that you've submitted earlier, you construct Traject classes with constructors, that accept some arguments.

Then all I can recommend is to use a collection like List to store all your output elements and then output them via iterating over the collection. Collections use generics.

Then describe please, what the program precisely must do under the hood. Because your current formulation of problem is similar to describing a TV like a "moving picture": under that definition, even...

System.out.println("Room 11 has H. DS as it's teacher ");
System.out.println(" Felix De Vliegher follows basis");
//And so on

This will do exactly what you want.

So you don't have to use your Traject, Cursist and Instructor classes? Then what's the task, precisely?

If you don't know even syntax, you shouldn't bother yourself with generics. Go here and read from the very beginning.

---UPD---
in fact, I can see no generics in the code.