With v.1.21 the game may be a bit easier because the Ai won't be trading amongst it self so much.
In regent the expansionist civs will take a lead, and will keep most techs to themselves. You can get ancient techs easily through trade. The only expensive ones are the governments, map making, construction and currency. Trade all techs immediately to expansionist civs because they will get them out of goody huts eventually.
Some notes:
Core cities are the 4 cities or so around your capital and the FP one. I dont' build FP too far away because then I will have 10 core cites if correctly space.
My info is most useful for large map with continents game on regent.
I also have found that sending 1-2 warriors of to some civ in the beggining of the game can help knock one whole civ out of the game.
My favorite regent civs are the Egyptians, Japanese, and Aztecs. The Aztecs are amazing. THey have good traits and an awesome UU. The only downside is the early GA. In one of my games I had 3 jaguar warriors. They all were elites thanks to popping up barbarian goody huts. THey took out 2 civs early on. The first had one city defended by a warrior, the second managed to get 2 cities but the second was undefended. The Egyptians are really good too. Their UU is okay but they have awesome traits for fast expansion. Industrious helps buildling tons of roads and irrigation to speed up expanding and with cheap temples you can take all the land.
Also I usually have my core cities spaced so there is no overlapping but most of my other cities overlap a few squares(not too many). With the Egyptains i spend ancient era expanding and beelining to literature and Great Libary. You can still survive the game without Great Libary but it helps out alot. They key to getting it is too build a few warriors, a granary, 3-4 settlers, and then start on the Pyramids and switch to GL asap. If the AI has literature(which it rarely does BTW other than expansionist civs), then it will switch as soon as Pyramids are lost. But with v.1.21 AI doesn't trade too much so you should have little compettition. Once the Great Libary is secure you can take it easy, lower your tech rate and continue building granaries, only in your first 10 cities, because it is a waste after that. The further out cities should build their own defender like every other city then a temple. If the cities are closer to the capital then build two defender, then settler and have it guarded by the second guy. I won't bother really with escorting until the map is getting crowded because the AI will start to take undefended cities.
If the AI demands tribute payup. They will pay for that later :die!: . By the time the middle ages come along most of the map will be covered up. I would build temples in most of the cities, and barracks, marketplaces, and aqueducts in top 10-15 cities. I would also setup one of the core cities(not capital) for a wonder by having it build palace until those Middle Age wonders come along. Here comes a hard part. There are some really nice middle age wonders, and its hard to choose. Sun Tzu's is nice but not as essential. Building barracks in your core cities should make up for that. IMO the essentials are Leonardo's and Bach/Sistine. The setup city should go for Leonardo's. I don't bother to get Sistine even though it gives more happiness than Bachs, but you need chathedrals, and on regent chatedrals aren't a big deal till you get over size 12. After Leo's is got quickly start palace in another city for Bachs. I let the AI get the techs till education then research music theory.
Now the late middle ages come along. There are more tempting wonders, Smith's, Copernicus, and Newtons. They are all good wonders, not the best but good ones. I would setup another palace to switch to Newtons. You should be able to get Smith's in your capital. AI doesn't make a big deal with Copernicus and you may get that too.
I don't war much in the Middle Ages. I make knights and take out the weakest bordering civ but thats it unless some civ has no iron, then take them out too. By the time cavalry come along alot of civs will have riflemen. Ofcourse with v.1.21 the scientific civs may not trade it off to everybody. The only way to beat riflemen is with overload. They don't depend on resources which is a problem. Cut off AI's horses or saltpeter to prevent them from having cavalry. Cannons don't hurt riflemen that much either. The key is to use MPPs. Sign them with everybody and make ROPs so the AI can use railroads and roads and go off to war. They should join and they will send tons of forces to fight. It helps especially since the AI is so stupid. They will send all their forces head on and often get slaughtered by riflemen. I've also noticed how attached AI is to its UU. In one of my games India even though it had cavalry still made so many war elephants to fight riflemen. Almost all of them lost. MPPs don't always win the war for me, but they do a few things. First makes sure you won't be backstabbed. Second you get an idea of AI forces and 3rd they will waste their troops on badly planned attacks on riflemen.
Tech wise I will beeline to get Theory of evolution. Often setup the palace for this one. I usually manage to get it in one turn with palace setup. So as soon as i have scientific method, i build the theory of evolution in one turn and next tech to research is Atomic Theory. Why atomic theory, because it is the most expensive one avaiable. Industrialization, sanitation and replaceable parts are cheaper. Next tech to get free is usually electronics anther expensive tech to start Hoover Dam(essential). At around this time i try to make some peace with the civ, but continue to make come cavalry but start to railroad and build factories. I go for sanitation and buy replaceable parts and corporation. Build factories, hospital and chathedrals to control happiness. Then go back to more cavalry making and start another war as soon as i get replaceable parts. Now i can use artilley which will knock down infantry or riflemen to a few hp for cavalry to finish off. I try to take another civ or two now. Then make more peace. By this time i have already had 1-2 leaders, with a non-militaristic civ. With Japan or Aztecs i could have had about 4. I do everything possible to get hoover dam. I use the palace setup or leader rush. Use first leader for army to make heroic epic and most others for wonders. If you get Hoover Dam the game is now in your control. Build more factories which will allow the automatic hydro plants from Hoover, and buy refining,steel, combustion. Research hard to get motorized transportation. Your top 10-15 cities should all be size 12+ and be building or have factories. Then start building more artillery and some infantry and when motorized transportation comes along build tanks.
With tanks and MPPs along with artillery take out another civ or two. By now you should have alot of control over your own continent. There might be another 1-2 left though. As soon as you get into the Modern era research fission asap. Put all your reasearch into it and setup palace or have leader ready. Build UN immediately and unless you are confident with your popularity hold off the vote forever, if you want or vote when the thing pops up every 10 turns. After fission go for rocketry and the sythetic fibers. Trade to get computer ASAP from scientific civs. Now during this reseach continue to build and improve. Alot of you cities should be bigger than size 12. Core cities around 25 and the others around 18-20. Factories in most and make sure you got temples, cathedrals (in big cities), libaries(not essential though), universities (same as libaries), rearch labs (again the same), factories, hydro plant (automatic), marketplace, bank, aqueduct, hospital. Don't build any power plants now until nucler powerplants and those in your core, reliable cities. Once you get modern armor build lots of them and now for space flight. AI by now has build Manhatten project and is building nukes. You build nukes too along with modern armor. I have been nuked before but not in my core cities, but two pretty big ones. I believe if you DON'T have Mpps then there is a less chance of being nuked because then all nations declare war on the nuker. If you have MPPs when fighting some nation then they won't hold back on those nukes. Destroy and be ready to take some damage from their nukes. Try to cut off the aluminum asap, and then their oil and later ther rubber which will cripple them. If you are nuked, nuke back because by now everybody hates that civ. I was nuked by India in my game and I nuked its captial and all its core cities. The Indians were stupid to nuke my secondary cities, when the should have taken out the capital with the ICBM. I have nuked cities which have resources in their radius to destroy roads even if it is a small city. In that same game India placed a stack of 40 modern armor, 20 tanks, 10 mech infantry, 10 infatry, some oboslete units also. They were two squares from one of my city's radius divided into 3 stacks next to each other. I nuked the middle stack. Yes the polluted my city but I managed to knock out a major force of their army without having to send in bombers and my modern armor taking their cities. I cleaned it up later. Also cripple all civs by having them war each other to prevent spaceships. Cut off aluminum sources. I was forced to nuke Rome and Moscow and some primary Russian cities to insure they won't build any spaceships.
Then after I'm satisfied with score, I usually build my spaceship and go off to a better world.