It's probably best left to a professional.
Sometimes they are glued on. In which case you need to use a solvent to dissolve the glue. Choosing the wrong solvent can also dissolve the paint and make a huge mess, or have no effect on the glue. It could also just be jammed really tightly. That might require, heat, cold, a penetrating lubricant, or all of the above to knock it free. Do that wrong and you could ruin the lens or shutter. Also, when removing lenses, you have to make note of the orientation and spacing. If you put a lens in backwards or get the spacing wrong, your pictures will look terrible. And lastly, cleaning the actual fungus can be a pain. Do it wrong, and you can damage the lens elements, or not clean it all off, and the fungus will regrow pretty quickly.
Basically, there's a lot to go wrong here. So it might be best to let a professional handle it. Though there might be permanent damage to the lens already, in which case you'll pay a bunch of money only to get back a sub-par lens. That would likely be about half the price of buying another lens. So it might be worth giving the DIY repair approach a try, and if you do ruin it, just buy another lens. At least then, you'll get a known good one (hopefully), and some parts in case you need to repair the new one in the future. So yeah, there are no easy answers.