Sitting correctly at a computer is the same as standing correctly and walking correctly. It is all about the pelvis and the lower back. My usual statement that it is all about the psoas applies here as well but the pelvis and the lower spine are more concrete to feel. The position of the pelvis determines everything that happens above and below with the legs, trunk and arms. The position of the pelvis and the ability of the psoas to do its thing are intricately linked.
Our lower back is referred to anatomically as the lumbar spine. This part of the spine, between the pelvis and the rib cage should always have a slight curve. This curve, which should be very small or gentle in its slope, is what sets human beings apart from all other mammals. It is the lumbar curve that allows us to be upright and walk on two legs. The lumbar curve is created by the psoas as we come up to stand and the psoas pulls the bones of the lumbar spine forward.
Sitting correctly at a computer requires the help of the psoas which, along with the hip bone, acts as a pulley system in the body supporting the upright position of the spine. When we lose the curve we lose all of our upright support. This is the key to sitting, walking, and standing.
Presumably you are sitting at your desk reading this (though I am a big fan of the standing desk). Put your hand on your lower back. Is it curved in or rounding back? Where is the weight on your pelvis? If I had to guess, your lower back is rounding backwards and the weight of the pelvis is slightly behind the sit bones. Try finding your weight just to the front of the sits bones (find the top of the sit bones and roll forward as little as you can). This should tilt your pelvis oh so slightly forward and move your lumbar spine into a gentle curve.
It is as simple as that anatomically. Everyone to some degree or another should be able to do this with their bones and feel the positive effect.
The main problem with this is that we are more than bones. We have muscles that are habitually tight and resist the changes we would like to make to our skeleton. While most people should be able to find their way to this correct sitting position, tight muscles will pull you back to where you were. It is just a matter of time. Sitting correctly at a computer requires length in a muscle at the back that will work hard to pull you back into your habitual position. This muscle is the quadratus lumborum that I have written about before and I will post more about them in the near future.