The Cairene taxi is at once a blessing to tourists, but can also be the cause of much frustration. Taxis in Cairo do not use meters, or any fixed system at all. All the taxis have meters, but will never use them. Every once in a while I have heard stories of taxi drivers turning on the meter when they have foreigners in the car, and then trying to charge them the price on the meter, which is much more than the usual. So if your driver tries to turn on the meter, or charge you the fare on the meter, immediately tell him no, and if he refuses, leave.
So, since there is no meter, how do the taxis work? Well, when you get in the cab it will be assumed that you know how much the price should be to where you are going. So, when you need a cab, stick your hand out, shout "taxi" and when one pulls up, tell him your destination. In general the taxi driver should not tell you a price, if he does, it usually means he is trying to rip you off because you are a foreigner. If the cabbie asks you "How much?" before you get in, tell him a fair price, and if he doesn't accept, leave, there are plenty of other taxis.
Once you get in the car, women do not sit in the front, the driver will take you to your destination and upon arrival, get out of the car, then hand the driver the fare through the window. Here is how you will know if you paid correctly. If the driver stays in the car and says the fare is too small and that he wants one or two pounds more, that means you paid correctly. Tell him that the price is fair and walk away, do not argue. If you start walking away and the driver gets out and chases after you, you probably paid too little. Give him a few more pounds, and then walk away. If you hand the money and the driver says nothing, you probably paid a bit too much.
You are a foreigner. Unless you speak flawless Egyptian Arabic, the cabbie will know, and in general you will pay more. A great way to lower the price is to talk to the driver. If you know any Arabic at all, even just "How are you?" use it! It helps. If you know none, and the driver knows some English, talk to him; it’ll drop the price. Also, if you pick up a taxi from any major hotel, that will add a few pounds to your fare no matter what. I realize all this can be frustrating for tourists, so here is a list of my suggested prices. 4.5 Egyptian Pounds=1 USD
Downtown to Zamalek – 3 LE
Downtown to Khan el-Khalili – 5LE
Downtown to the Citadel – 6LE
Downtown to Mohendiseen – 6LE
Downtown to the Pyramids – 12LE
Downtown to Giza – 8 LE
Airport to Downtown – 35LE
Downtown to Airport – 30LE
Those are very fair prices, and about what I pay. However, if you want to avoid any arguments at all, add a few pounds to those fares. Also, if you pack the car full of people or there is a lot of traffic, add a pound. That should do. Good luck!