Unless you have a house cat i.e. a cat that simply does not leave the house, then getting fleas at some point in its lifetime is an inevitability that you have to live with.
You can help your cat by applying flea drops to its fur regularly. You vet will be able to recommend a suitable product, normally these are placed on the back of the cats neck (where it can't lick it off), and this normally last for about four weeks. Other methods include using a flea collar (the collar is saturated in a chemical that repels fleas), or an injection that is available at your vets, this repels both fleas and ticks.
Even taking steps to prevent your cat from getting fleas can sometimes not be enough. Regular grooming will help to get rid of any fleas that may have been hiding in your cats fur (although this won't help with an infestation). If you do find the odd one or two fleas in your cats fur, a good idea is to buy a nit comb (a small silver coloured comb, that is used for extracting head lice from children's hair). The nit comb is ideal due to its tightly packed prongs. Daily groom your cat using the comb and you'll be able to get rid of any adult fleas on a daily basis, without putting any more chemicals on your cats fur.
In many stores you can get a multipurpose flea powder. The idea of this is to apply it to your cats fur and to your carpets, killing all traces of fleas. However, you may find your cat objects to you applying powder, if this is the case you can still apply it to your carpets to kill any fleas that may be laying eggs in it.
There is also a spray you can purchase to treat fleas, however this is not very popular with many cat owners due to the noise of the spray scaring the cat, and therefore the cat associating the spray with something bad. However if you cat is not afraid of these sounds, then the spray is very effective.
Often it can be your own house that is the problem of the flea out break. Fleas can lye dormant for years in the carpets, until a suitable animal comes along, which causes them to hatch and start causing problems, this can be a serious problem, if you've moved into a new house where the previous owners had a cat or a dog. The best way to treat this is with cleanliness, vacuum your floors and carpets daily, you can apply a flea killing powder that is designed just for carpets, however you normally have to leave this for sometime before you can vacuum it up, so apply it when your going to work, making sure your cat is outside and the vacuum it up when you get home. Another more natural method, is applying Juniper oil to the filter on your vacuum, fleas don't like Juniper oil, and the scent will be spread through your carpet when you vacuum, this isn't an over night success, but will help in the long term battle with fleas.
There are a few more non-chemical methods of removing fleas from your house. A new favourite seems to be a lamp and sticky paper, these are a kit you can buy from most pet stores, there is a lamp that is placed in a room with sticky paper attached, and when the fleas sense the warmness of the lamp, they believe it is a passing cat and jump up to latch on, only to be surprised by the sticky paper, which they end up stuck to. This is a non-chemical method, which will attract adult fleas, however this will not kill the eggs or larvae that may still be living in the carpet, so you may also need to use this in conjunction with another treatment.
You can also try using a sonic system. These are normally devices that are plugged into your mains electricity. They normally have 2 settings, one can be used for vermin (rats and mice) although don't use that if you keep small mammals, like hamsters and gerbils. And the other setting is for insects, the sonic noise, that cannot be head by humans, is an excellent repellent for insects, it takes about 2 weeks before the results can really be seen, but generally speaking you'll rid your house of most crawling insects.
You can also try applying lemongrass essential oil to your cat's collar, fleas do not like this scent and will often leave your cat at the earliest opportunity. The only problem with this method, is that often cat's do not like the smell of lemongrass either, and as cat's have a very sensitive sense of smell, it may be worth only applying one or two drops to the very back of the collar, thus saving your cat from having an over powering scent following it everywhere it goes.
One method, which most owners would only use as a last resort, is bathing your cat. Most cat's will not thank you for giving them a bath, and it can be very distressing for them. If you have a cat the is quite content with water, then bathing your cat should not be too much of a problem. You can buy specialist pet shampoo from most pet stores, however if you are unsure, then use a non-fragranced shampoo with added tea tree essential oil. Tea tree essential oil is anti-bacterial, so as well as cleaning your cat, any wounds that may have been cause by fleas, such as over scratching, will be mildly disinfected by the oil.
If after try all the methods above you are still having troubles, the only plan you really have left is to visit your vet. You vet will be able to advise you on a course of treatment to get rid of the fleas, and in severe cases you vet may want to keep your cat in for treatment and observation.