I took my coil out myself. It had already come out from where it should be and I was in a lot of pain. So for me it hurt a bit but was worth it because of the agony I was it. If it is in place I would not risk it and would go to family planning.
i had a coil removed by a doctor, didn't hurt at all, was really quick, much easier to get out than put in, she didn't use any of the equipment they use when putting them in either, just got hold of the strings and pulled. she said that the arms of the coil are made so they bend upwards as it comes out.