You don't. Fungus which comes in many forms an colors is absolutely essential in the beneficial breakdown of your compost's organic matter. If it is unpleasant for you to look at just place a thin layer of decorative green moss...which can be purchased at any craft store...on top of the surface.

Loosestrife given that this person is talking about the compost their potted plants are in I'd suggest they do need to treat. Fungi grows in moist, cool, dim conditions. If you water too frequently, or if you use a water-retaining potting soil, this contributes to the problem. The easiest thing would be to repot your plants in fresh compost, make sure you wash all the soil from the roots or you could continue to have the problem.

Hmm,well it would have been very helpful to see a clear photograph showing the pots and the surface of the compost - if you have used multi purpose compost with plenty of lumpy bits of undecomposed woody parts, then fungal growth on that is highly likely, especially indoors, and this type of fungal growth will not harm your plants. The other possibility is you are overwatering, depends what the fungal growth looks like and precisely what its growing on, what the plants are in the pots and so on. Insufficient information to give a good answer, we can only guess, which is why the first two answers are quite different from one another. If you can add a photograph, you may get a more definitive answer.

In my experience, the main causes of "fuzz" on potting compost are overwatering--primarily watering too often, so that the compost surface doesn't dry between soakings--and/or poor air circulation.
The potting compost may also be to blame, as Moon_grower said, if it is very fine textured. I would take a pinch of compost and rub it between my thumb and fingers. If it left a muddy or peaty smear on my fingers, I would find a better compost, and change it out. It's not a given, but composts based on coir are less likely to get the fuzz than those based on peat.

Or another solution would be a simple quick fix if you want to avoid taking out, changing ect which has the possibility of destroying root, and or root hairs and having your potteds going into a bit of shock....just take a spoon or butter knife and scrape it off of the surface whenever you see it developing.

When its all sorted you might consider putting a layer of coarse grit on the surface of the compost -that should prevent it happening again, or at least greatly discourage it.

Agree Stera...

Is it fungus and are your plants thriving are the questions that needs addressing first, I too have white on the surface of the compost in some of my indoor plants, which are very healthy I might add, its caused by the hard water we have around here, bit like one gets in the kettle and washing machine, obviously don't know whereabouts you live, its recommended to use rainwater but its winter and the butt is down the yard, easier to use the tap in the kitchen, my plants are thriving, flowering and some are donkeys years old, whilst they continue that way I do not worry about it, as said rub the compost between your fingers and see what happens, if its like mine it will just crumble, if its a fungus it will smear as Tugbrethil has said which is a different matter altogether ...

Well, my smear test is to find out how much clay/silt or highly decayed peat there is in the potting compost. A large amount helps outdoor plants to avoid drying out quickly, but keeps the soil surface too moist for too long on indoor plants. Surface fungi on indoor compost usually takes the form of a whitish or grayish fuzz, similar to bread mold--many of the offending species are actually related--or thin threads or sheets of a white or yellow mushroom-like substance.
In the USA, potting compost is sold as potting "soil", never mind the fact that practically all are actually soilless mixes. Generally, the "all purpose" or "multi-purpose" mixes are too fine and peaty for good houseplant mixes, and are subject to visible fungi, and fungus gnats. Mixes labelled for African Violets or Cactus have a better crumb structure, and work much better for indoor use.

Tug - in the UK, multi purpose potting compost is no longer fine and peaty and hasn't been for about 5 years or more - many contain no peat at all, or just less than 10%, and are mostly comprised of composted materials (well, loosely, a lot have partially composted material within the mix and many need seiving prior to use because of the rubbish within). The reduction in the use of peat is purely ecological, and enforced by law - doesn't sound like that's happened over there from your description.

Hi Bamboo, bit late but Happy New Year to you anyway, hope all is well with you.....

Thanks Lincslass, here's hoping for a good one for you too...

A belated Happy New Year to you from me, too, Bamboo! :)
As for the peat, yes, laissez faire capitalism remains the watchword, precariously supported by the remaining peat beds in Canada and western Washington state. Sooner and later that will change, so I am always looking for alternatives for the store. Unfortunately, all of the mainly composted brands that I have tested so far have been of very poor quality--muddy, smelly, and/or gnat-ridden. Ah, well, someday.... :]