Just finished Egypt in 1480, and I'll descrbe how I won.
(Forgive me that my writing sucks.)
Plan
The very first thing we should do is to plan. If we start playing the game right away, the likelihood is that we will make some nonsense decisions. Here is the plan I made for this time:
1) Cities: Niwt-Rst (capital; 1N of the starting tile), Per-Wadjet (1W of Wheat), and Yebu (2W of Gold) will be built. 2 Greek (Athenai and Byzantion), 1 Babylonian (Babili) and 1 Indian cities will be conquored by a chariot-rush. 1 more city will be captured or built so that there will be eight cities.
2) Legendary cities: Niwt-Rst, Babili, and Athenai. There is no need to worry about respawn, since it is presumably possible to win the game before anyone gets Nationalism.
3) Civics: Early civics - Monarchy, Slavery, and OR. Later civics - Monarchy, FS, Caste, and Pacifism.
Early game
I built Niwt-Rst (1N of the starting tile) and sent the warrior to get goody huts (4 total). I got small amount of cash, tech (pottery), map, and a warrior. Niwt-Rst built worker, worrior, worker, granery, settler, and war charriot. I kept checking mercenaries after I got cash from a hut, and I was lucky to get a war charriot for the hire cost of 21 and maintainance cost of 2. The two war charriots invaded Babylon and captured Babilu (turn 60) and razed Ninua (turn 61). The hired war chariot was then fired. I built the Pyramids (turn 69) and started preparing for invading Greece. I surprise-attacked Greece from the sea (Per-Wadjet whipped a galley) and captured Athenai (turn 81; landed turn 80) by two war chariots. Loaded the war chariots on the galley (turn 81), gave them a turn to heal, and attacked Byzantion from the sea (amphibious attack) and captured it (turn 83). One thing to note: before invading a civ, check mercenaries. If you do not hire them, your enemy might hire them. Oracle gave me theology (Christian holy city!), and I got Mining, Hunting, BW (I had to research it a bit), Alphabet, and Monarchy through trades with Carthage, Rome and Persia. From here, everything is self-explanatory: make important buildings (e.g., granaries and libraries), trade techs whenever possible, build some units and prepare for barbarian hordes, build wonders in cities which will be legendary, and so on. Persia and Rome decleared war on me, and Ethiopia became my vassal. Nothing special. But one thing to note is that you should constantly ask for a small amount of cash if a civ is pleased or friendly with you. It helps your research and might avoid a war.
Mid game
I partially researched paper and philosophy and kept a GS. I don't remember exactly when, but techs become chaper a little bit before Arabs spawn. After Arabs spawned, I finished researching those techs and used the GS to partially research Education. I have been unlucky that until the 10th C, I got only one GA, which came from Music. I finished researching all the techs I need in 960AD (see the pic below; Constitution came from Liberalism) and switched the civics to the four I have planned. Unfortunately, I have underestimated the terrible instability of Egypt, and I lost Babilu due to instability during revolution. I reloaded back to few turns ago (it did not give me anything special but a chance to switch civics differently and to whip few more buildings, but if it constitutes cheating, please don't add my score on the record). This time, I switched to FM and Pacifism before finishing researching Liberalism (when I was not so unstable), and then I switched to FS and Caste after I whipped some temples and courthouses. My stability was about -19 most of the time, and I really regretted that I razed Ninua. Later I adopted Viceloyality, since I got an extra vassal, Mali. With 0% research rate I also started researching Optics. Neither Aztec, Inca, nor Maya (alive!) became my vassal.
Late game
Golden ages (from the Taj Mahal and GPs) really improved my stability for a while. Nevertheless, the stability went into unstable in 1350 AD. And there came an unlucky event - plague. Well, I guess Rhye will fix it, since it's certainly an exploit, but there is a way to avoid a plague. That is, when plague hits one of your cities, gift the city to another civ. It is usually more costly than plague, but in this specific case, it's helpful. In order not to lose any essential city, I did that. Niwt-Rst became legendary in 1450AD. Babilu became legendary in 1460AD. My golden ages ended in 1455AD, and the stability became collapsing in 1465. There were three more turns until Athenai would become legendary. I prepared a galley with units and removed all the units from every city except the capital, so that I can recapture them quickly. Fortunately, my empire did not collapse and I won in 1480AD.
Summary and other stuffs
So, there were some lessons I learned. First, never raze a city. -4 stability point is extremely large when your empire is shaky. Second, it's not good to quickly build the Pantheon and the Leaning Tower if the Greeks are already dead. I got way too many useless GPs. Third, I totally forgot trading with East Asian civs. They usually do not OB with me, but Japan usually declears war on China about twice in a game, so, in such occasions I could have decleared war on one side and OB with the other side (depending on who's the master of Khmer). I must have been able to obtain Silk and Banana too.
I have made two decisions which can be seen as cheating (reloading) or exploit (avoiding plague) as noted above, and I must have not been able to win without them. I was also planning to play Egypt with four cities, since it seemed to be better in terms of stability. However, it turned out that the greatest amount of instability in the current game came from Economy (-49 at the end), and Expansion (-24) was no so problematic given that there was a great positive from Cities (+32). The last thing to note is that a golden age might actually harm our stability in a long run, since there will be a huge drop in commerce when it's over. It might be a good idea to win the game before the golden ages are over.