For all the following: YMMV*, caveat emptor, no responsibility taken for advice given, you decide whether to try this at home. It may even work :-). Be aware that damage may already be fatal and/or that fatal (to the lens) damage may occur along the way. Best attitude is to regard the lens as a writeoff now, with anything you can gain from it by the methods below being a bonus.
Fungus in a lens will always degrade the image but the amount of degradation may be invisible to mere mortals or may make the lens completely unusable by any standards. Often even a very visually significant lens defect - such as a chip or scratch, will not be instantly obvious in final images to a casual observer. Experts will usually be able to detect almost any defect (or say they can - mere mortals will not be able to tell if they are correct :-) ). Also, lens settings will affect how much a given defect affects a given image.
In some cases the advice given in 1a and 1b below will transform results from generally unacceptable to generally acceptable. In other cases they won't. Only trying it will tell you how good a method will be.
The best advice (but too late :-( ) is to never let it happen. Fungus only grows in moist conditions. Keep your lenses in a well ventilated dry location with dessicant sachets. However -
If it's inside the lens there are two options (apart from disposal). Unfortunately, while either may work, neither is certain to work well.
1(a) Shining UV (ultraviolet) light into the lens for an extended period will "discourage" the fungus, how well and how long is uncertain. Simply leaving a lens with iris fully open on a sun facing window ledge in a dry location for weeks to months may produce good results. Cap lens at rear, and tilt so that sun shines into lens during sunnier parts of each day. (Be ware that sun shining directly along the axis of the lens or close to it may focus light onto end cap and melt it - unlikely but check point and degree of focus.) I tried this procedure with an extremely old Minolta 50mm f1:1.4? manual lens and achieved tolerable results. I simply left the lens as above for many months and when I next looked found that mold presence had been very substantially reduced.
1(b) Light from a germicidal (short wavelength) UV lamp may be used in place of sunlight. This sort of light can blind you or damage your eyes permanently if looked at for substantial periods and can cause "arc eye" - painful but usually temporary inflammation of the eye. This does not mean you should not use such lights at all - simply that they need to be used with due respect. These lights are available from many sources for many purposes and can be very low cost.
Note that "black light" UV light is not suitable for this purpose. It is longer wavelength and not very biologically active.
Note also that the short wavelength high energy UV (which is why you are using it) from germicidal UV lamps will also degrade other materials such as some plastics and miscellaneous other material - including, possibly, parts of a plastic lens housing. This depends on material, distance, light energy and exposure time. YMMV but caveat emptor - ie know that you are using a tool with sharp unguarded blades (even though you can't see them) and use with due caution.
All the above may put some people off UV germicidal lamps. If so, that's good. They are a great and useful tool but not suitable for use by careless or unthinking people.
2 . Dismantle and clean. If the lens is so degraded that it is unusable and if the method above does not work well enough then the lens must be dismantled. If the lens is otherwise a 'writeoff" and you are competent mechanically you may wish to try this yourself. Reassembly of a lens capsule is considered to be an expert task and realignment on reassembly may require arcane knowledge. This is why qualified lens servicing people are still in business and cost money to use.
Fungus often attacks lens surface coatings and may etch the glass itself so the lens may be noticeably or fatally degraded regardless. How much the may/may/may applied in your case is tbd. Some lens cleaning works very well indeed. An aficionado and a good MTR test will probably tell you that something has happened but the results may be very tolerable in practice.
You will find articles on the internet on lens cleaning methods. I read a paper by either Zeiss or Leitz that suggested that cigarette ash makes an excellent fine cleaning compound (!!!).
Added: Member 19602 made this comment - as he has left and comments may too I'm adding it to my answer.
On April 7th 2013, once was member 19602 said:
- I can tell you with absolute certainty that the Leitz recommendation is not a sealed container with desiccant but an area with constant air circulation. I used to be with Leitz Germany.