Here is my strategy slightly improoved after reading some posts on this forum.
The golas are:
1. Make 2 great cityies in early game
1.a. Found at least 1 religion in early game
1.b. Build at least 3 wanders in the early game
2. Keep up with the AIs in science
a. Go for tech with bonuses, such as liberalism, Phisics and so on.
b. Go for tech necesary for the space race.
3. Win the space race.
If you manage to fulfill all those goals, step by step, you can win the game with random civilization, no matter the speed, no matter the size or the type of the map, not being agresive (no need to declare war).
But how can you achieve those goals?
1. Make 2 great cities in early game.
First, usual place the fisrt city right on the spot. Usulay there is the best place to build. The ideal first city wold have around it either flood plains or oasis or other tiles that can provide 3 food and some gold from the beginig of the game. If you don't have the ideal city, no problem, you can catch up later.
What would you build first, depends on the surroundings and the techs you start with. If I start with huntig, I build the second scout. If I start with fishing, and I have a costal city and probably some sea resouces nearby a build workboat firs, but most of the time I end up building warrior.
If I have "the ideal city position", it will grow very fast to size 3. Than I start to build the settler. If is not ideal, I start to build a worker at size 2. And do some research needed to improove some bonus tiles around.
The first tech for reserch depends of the civ you play with, and of the general conditons. If I start with Misticism as starting tech, I go straight to Politheism, if not I start reasearch Misticism first then researching Politheism. It is possible, this way to found the Hiduism. If I don't have a spiritual leader, I don't convert to that religion just yet. Depending on conditions you may need to research some worker techs (agriculture, hunting, animal husbandry) or fishing. But I always head for Monotheism. It is the 3d religion that can be found and usualy the AIs don't rush for it. There is 99% chance that you will found that religion.
While the city grows and the research is done, I explore the surroundings and I am looking for at least one of the vital resources (stone and/or marble) if it is not already within 3 tiles from mi city. If you can't find neither stone or marble, this strategy will not work and sould find something else
Next thing I am looking for are other civs and the best place for my second city. Ofcourse goodie huts are a good chance to get some free techs or units, or at least money. That is why I prefer to train second scout if it is possible insted of warior.
When the city is size 3 I start building the settler. If I have allready spoted de good place for the second city, I prepare the path to get to it.
By the time it is being built set the research for monotheism but be careful to finish this research only after the second city is built. When the research on Monoteism is finished the Judaism will be founded in the second city, giving it a cultural boost. Definitely convert to that religion.
By the time you do all that, you have figured out if you are alone or note on that continet (island), or who are your neighbours. Knowing that you can decide what to research next, a military tech or priesthood. If I don't see an iminent threat I go for priesthood (to be able to buid the oracle). If you go for military, go for BW, to chop forests, that is imperative if you don't have acces to stones.
In the first city, after the settler you may whant to build some defence (if is not already there). Build an warior and then go for the piramids, but be sure you have at least one worker.
After secured the second city, start building Stonehenge there. Be sure you build a quarry on stone tile and connect it to the capital. If no stone, don't build quarry on marble, go for choping trees.
You mai fail building Stonehenge, but try not to fail the Piramids, it is vitale in this strategy.
Finished one, start the another wonder. Parthenon is a good option for the capital and the oracle for the second city.
If you have both marble and stone in your city radius it is a good chance to build all 4 early wanders, if not, you will probably build only 3. From now on you have to concetrate on exploiting your leader skils.
2. Keep up with the AIs in science
To do that you need to expand your borders and to maximaze your commerce and science. Trading technologies with other civs is a must so researching alphabet should be a piority.
Having early 2 wonder cities is very helpfull. Try to maximize the great persons production. If the leader is Philosofical, this should be the main focus.
Don't bother to build large armies. At this point it would be suicidal to go with an aggresive war. Concentrate on defensive units. Build some offensive units for the barbarian cities if necesary. Keep in mind that wile the AIs build and stack their units you can keep building some cities. Make friends, if is possible, by spreading your religion. Keep good communications betwin cities and be preapared for eventual defensive war.
Actualy, a defensive war may be profitable, after a wile, the civ that declared war would be willing to negociate the peace, be sure you take all techs available and some cities too, but don't be greedy, just 1 or 2 cities would be enogh.
Keep your economy on track, build courhouse, and Forbinden Palace. Build everiting that helps making more money or more research.
Go for Liberalism when possible and get the free tech Nationalism or Astronomy depending on the situation. Always check the progress of the other civs and just keep up.
Keep building wonders whenever it is possible.
Use diplomacy often. Trade resouces, and techs. Try to make friends and try to make the other civs to declare war to eachother, this will slow their research and building, as they will keep building only military, and research military, and the upkeep will keep growing
3. Win the space race.
To do that you must haveat least 4-5 cities with high production and you need to start early. Forget about techs that don't help you with this goal. If you need them, you can consider building the internet. But is better to concentrate on space race tech. Keep trading with other civs and, keep the diplomacy. Keep waching the others progress. If some civ is dangerously close to space vicory, you may rather consider make them declare war to others, or others declare war to them. All AIs have some enemies, and mot probaly you are friend with one of them. No matter the cost. Just make them beat each other. This will give you the chance to fhinish your space ship first.