most strategies tend to focus heavily on the early game, because that is the most predictable part of the game, or the easiest to plan for. Most of the good strategies that are written try to set you up with a solid foundation from which you can best decide how to proceed.
That being said, you can't talk about the mid-to-late game without saying that you must establish a good start, or something workable. This can be done by expansion, rushing, or a combination of the two. Not many civs are great at turtling in a few cities, and even with those civs (pretty much Greeks and Egyptians w/ Collosus), you still would do better to expand, if not early, later on in the game.
Not all civs have bonuses that are great in the industrial or modern. The French, Aztecs, Russians, and Egyptians are all great examples of civs that don't have bonuses that will win you the game late.
Basically, you want to expand out to as many cities as you can defend, usually at least 8, preferable 12 or more. The main expansion phase should be over by around 0AD, give or take a few turns, but you should still look to expand if it doesn't slow you down.
If I'm going for domination, then I'll choose what type of domination victory. If I have low production, then it's probably a bunch of vet legions. If I can get them out fast enough, knights are great. Against the AI, knights will probably work till around 1000AD. Elite players can get knights in the BC years, and win a lot of games online like that, but you don't need to know how to do that, and sometimes it's risky to sell out on costly knights early in the game.
If you are close in tech with the other civs, but you are doing a little better in tech, then you may want to wait for tanks, or get Advanced Flights (thus Bombers) from Oxford University. Tech up to Industrialization, then University, and dont' get any techs that cost more beakers than Industrialization, and then produce the Oxford University, and you will get Advanced Flight faster than you can get tanks.
For the other types of wins, it takes a lot of expansion. The more cities you have, the faster Economic and Tech victories will be. Civs like the Greeks and Chinese can get tech wins fast, due to half priced libraries. Just expand like crazy, get to 14 techs, and then get 20 hammer libraries in all your cities, switch to democracy, and just like that, you have about triple the tech you had before.
Economic victories are the fastest non-domination wins, especially with 50% gold civs like the Aztecs, Spanish, and Zulu. But, 50% gold bonus also means 50% inflation. You'll be paying a lot more to rush buildings and units. So, stop teching before you get that bonus, build up a little gold, bank some hammers, and rush a few markets, and then get the bonus. Economic wins really only need industrialization, corp, gunpoweder or whatever you need to defend, and Communism. Rush a factory early in one of your cities before banking gold, and then start banking hammers for the World Bank. Communism will help finish off the wonder if you haven't by the time you get 20,000 gold.
Culture wins are the slowest of all victories (execept for maybe with the Romans). You need a lot of production. Having a high culture count can help, but the fastest way is to build a lot of wonders. Usually when I'm winning a culture win, it's with about 10-12 wonders, and the rest settled GPs, with maybe one or two flips.