I think one of the things I love most about Egypt is how easy (and cheap!) it is to get around. I can go from one side of Cairo to another alone, and it only involves one or two transfers. Once you get over the initial shock about what the transportation actually is, it's easy! Here are the main forms of public transportation in Egypt.
Tuk Tuk.

Tuk tuks are three-wheeled vehicles and are used to get around a small area. For example I used to use them to get around my area (6th October City). These are only easy to use when you know where you're going. Some drivers dont know all of the roads. This form of transport isn't actually very safe, and I have frequently heard about people having accidents in them, though, thank God they weren't serious ones.
They are cheap, but also not the cheapest option, which is why I stopped using them if I can use the trucks instead. a typical 5 minute journey costs between 5 and 15 EGP. It sounds like nothing for people in Western countries, but if you compare it to the average Egyptian salary, it is a medium price. BUT, I would not advice anyone to use tuk tuks unless you are with an Egyptian, or you have good experience in Arabic AND haggling. All of the times the driver knew that I am British I got into some kind of trouble, whether it was the guy hitting on me, or trying to charge me too much. I'm shit at haggling. I'm lucky because I wear the veil, and since there are a lot of Syrian refugees living in Egypt, most people just think I'm Syrian (they're quite pale- skinned and have blue eyes and blonde hair.) But the funny thing is, people get very confused because I look Syrian, but speak in an Egyptian dialect, so I STILL get asked where I'm from.:D
Truck (not sure of the name, they just call it "3arabya" (car))
This is one of the cheapest ways to get around (1.5 EGP for the trip). But the problem is that they're on set routes. So you can't take it if it doesn't go to where you want to go. The only two times I take this is when I'm going to the bus station in the town centre (Hosary Square), and when I'm going to the local market (souq). You may use this if you're a foreigner, but be prepared for a little harrassment (sexual or otherwise). I once took my European friend who doesn't wear the veil, on one of these, and the driver wouldn't stop going on about how he went to Italy once. He just kept repeating it.. Just make sure you know enough Arabic to ask if they go where you want. I will include this in a "Useful Arabic Phrases" post.
Microbus.

Microbuses are my life. haha. I remember the very first time I got in one of these with my husband, I was terrified! Obviously they don't look legitimate for anyone coming from the West. They look like they will fall apart, they don't have any signs on them, they all look the same, money is just passed around the bus to be paid (which gets extremely confusing) and they are driven so fast and recklessly you are sure you will die.
However, once you've been a couple of times, it's so easy! You don't need signs on them because the drivers are shouting out where they're heading, and you can always ask anyone which bus to take for your stop (Law SamaHt, 3ayz/a arooH____ (Excuse me,; I want to go to____)). Payment is easy, the driver will say the price, and you just have to pass your money forward and say (WaHed (One)) money and know how much change you need. It is in this circumstance that I find the men here to be such gentlemen! They always make sure I took all of my change :) When people pass money forward, they will say how many people and maybe to where. You just pass the money forward and repeat what they said. Then if you also don't know where you need to get off, you can ask the driver. ( Law samaHt, 3ayz/a anzil 3and_____ momken tet'olly anzil imta? (Excuse me, I want to get off at____ could you tell me when I should get off?)
This form of transportation is usually fine for Westerners, my European friend used to take them regularly and had no problems. I once took my British friend on one and some guys just practiced their English on us when I asked the price ("two pounds" he said) and also when they wanted to get off ("Excuse me") which I thought was sweet. However, I have been harassed a couple of times on the microbus. The annoying thing also is the way they did it- the first times I doubt myself because they do it so discreetly (like taking up your personal space) but you just have to shove them off. But like I said it only happened twice, and I've been taking these busses a lot over the last two years.
The prices are cheap, I can get from 6th October to New Cairo area (2 hour trip) for 8.5 EGP. And the price to get to somewhere closer, such as Downtown/Tahrir Square/Zamalek/Mohandiseen (40 min-1 hour trip), is 4.5 EGP.
Government busses.
These are looking more like something we take in England. :D haha. Similar to microbuses but a little cheaper (usually 2 EGP for the trip) there are many different routes, which is usually written on them, but unless you can read Arabic I would simply ask the driver if they're going to where you want.
P.S. These are hell in rush hour.
Metro
I don't take the metro much at all, only if I'm going to Maadi or Ain shams. From what I know of it, it is crowded all the time and at worst at rush hour (like everywhere else in the world.) There is a separate carriage for women which decreases likelihood of harassment. There is often people selling various bits and bobs cheaply. I don't like taking the women's carriage because the women basically fly everywhere when we come to a stop or speed up a bit. Not aware of the prices because I've never gone on my own, but I hear the prices are about to go up (like everything else.)
Taxi.
Don't worry, Egypt isn't medieval :D Taxis are available everywhere. Use them like everywhere else. Just a word of caution; make sure they're running the metre first, and it is also useful to ask a local roughly how much the trip SHOULD cost (because a lot of people get grossly overcharged.) Taxis are SO much cheaper in Egypt than in the West!
Uber/ Careem.
Uber is a great alternative to taxis here to avoid being ripped off and other problems. Careem is a local version of Uber and they also have an App. :)
If anyone has any questions or suggestions, please comment below. Have a great day. :)