I am sitting on the computer. - This is not correct because it means that you are using the computer as a seat.
I am sitting in front of the computer. - This is correct, with the emphasis being your location in relationship to the computer. It doesn't necessarily mean that you are using the computer to do work.
I am sitting at the computer. - This speaks of your location as well, and it likely means that you are typing, reading, or doing some type of work using the computer.
Student or Learner