Science
In most respects this is not all that different in Civ 5. Most of the techs are the same, there is a tech tree that is pretty similar, and you need to keep up in Science for any victory condition you are seeking. You may want to just beat your enemies into submission, but if you are using Chariots while they have Tanks, you aren’t going to have success. But also it is obvious that if you are going for a Science victory, you need to really focus on this. So many of these tips should be followed for any victory condition, but should be mandatory if you are going for a Science victory. The mechanics of researching technologies is that you have to accumulate a certain amount of Science to discover a new technology, but this amount goes up over time, so you have be continuously looking to increase your output of Science to keep up. for instance, one of your first Techs would be Pottery, which has a cost of 35 Science. But in your Capital city you get 3 Science from your Palace, and let’s say you have a population of 2, so you are generating 5 Science per turn. That means you will research Pottery in 7 turns. But the Education tech costs 485 Science, Astronomy costs 780, Scientific Theory costs 1650, Plastics 4700, and Particle Physics 6000. These are all key techs to advance your Science to a Science Victory. So you can see that you need to be continually increasing your Science.
To start with, Population=Science. You get one Science for every one point of population. That does not, however, mean that you need to have a lot of cities to get there. 4-5 well developed cities are quite sufficient, and adding more cities can cause Unhappiness problems. Since higher population itself can cause Unhappiness there is no good reason to add to the problem.
Buildings
The next boost you can give to Science is by building city improvements. The first, which comes early in the game, is the Library, which is available once you research Writing. A Library boosts the Science output of a city by one Science for every two citizens (roughly a 50% boost, rounded down), so building those early pays off. Because advancing through the tech tree is a process of accumulating Science, the earlier you can get these boosts the better. The other population-based boost is the Public School (available when you research Scientific Theory), which also boosts Science by one for every two citizens, and also offers a Specialist slot for a Science Specialist. And since more population means more Science, the Granary (available when you research Pottery) is a good building because it helps to grow your population.
There is one other building worth mentioning which is the Observatory (available when you discover Astronomy). It doesn’t depend on population, but on location. You have to have a city that is located directly next to a Mountain to build this, but it adds 50% to the Science output of the city. Mountains are otherwise useless (unless you are the Incas), but if you want a Science boost and happen to see good location (the ideal spot is an isolated mountain that is not part of a mountain range so you don’t lose farming and mining production) this can be great boost.
Scientist Specialists
You can at a certain point take some of your citizens out of the farming and mining and turn them into Specialists, but you have to have a slot for them, and those slots come in buildings as well. We’ve already mentioned Public Schools providing one slot. Universities (available when you discover Education) provide 2 slots, as well as boosting the city output of Science by 33%. The other Science building, which comes late in the game, is the Research Lab (available when you discover Plastics) which adds another Specialist slot, plus 4 Science, and then adds 50% to the Science Output of the city. It comes too late to help much in most of the Tech Tree, but is essential to research the Space techs, which are very expensive.
Wonders
The first one to try for is the Great Library. It gives you a free Library in the city, +3 Science per turn, and a free tech. Use the free tech to get an expensive tech like Philosophy. Oracle provides 1 Great Person Point per turn towards a Great Scientist. Hanging Gardens provides +6 Food per turn (boosting your population), and a free Garden which boosts your Great Person Points by 25%. Leaning Tower of Pisa increases your Great Person Points by 25% in all cities, plus a free Great Person of your choice when you build it. Porcelain Tower gives you +50% from Research Agreements, plus a free Great Scientist. and Hubble Space Telescope provides two Great Scientists, a free Spaceship Factory in the city where it was built, and +25% production for spaceship parts.
All of the above are World Wonders, which means you are in competition with other players to build them, and only one player can be successful in each case, so you won’t get them all. You can sometimes rush a World Wonder by “chopping”, i.e. using your workers to cut down Forests for added production, but you need to have high production cities to build Wonders in general. There is one National Wonder to focus on, though, the National College. Every player can build their own version of any National Wonder. The National College can be built only when you have a Library in every one of your cities. Your strategy should be to build it as soon as possible, so don’t build more than 3-4 cities before you get to this. It gives you +3 Science, plus an increase of 50% in the Science output of the city you build it in.
Great Scientists
As you work on your Science you will accumulate Great Person Points towards getting a Great Scientist. Some wonder produce Great Person Points, and all of your Science Specialists produce Great Person Points as well. As these add up you will suddenly see a Great Scientist appear. In the early game, the best thing to do is use this Great Scientist to build an Academy. Move the GS to any tile within your city and create the Academy there. It will yield at least +8 Science, bu there are also modifiers that can add to that. The alternative which is better later in the game is to use the Great Scientist to get a free Tech discovery. The reason is that early in the game that +8 Science is very significant, and it can accumulate over time. Combine that with things like an Observatory and a University that increase the city output and it can add up nicely over time. But by perhaps the Medieval Era, and certainly the Renaissance Era, you start running out of time for that accumulation. Meanwhile, the techs have gotten so expensive that a free Tech is the better option.
Research Agreements
These become available once you research Education. You have to have a Declaration of Friendship with the other player to create one. You each put a certain amount of gold into the pot to fund the research, and after a period of time (usually 30 turns) you each get an amount of Science from it. The way it is calculated is based on the partner that produced the least amount of Science during the agreement. From a science standpoint if you are ahead in Science it probably won’t benefit you to enter into the agreement. But it does build your relationship with the other player so I wouldn’t avoid them altogether. If you are behind in Science it can help you, of course.
Policies and Ideologies
Given that you should probably be building tall (4-5 cities) instead of wide (8-12 cities), it makes sense to start out with Tradition instead of Liberty. But once you get to the Renaissance you will want to enable the Rationalism tree to maximize your Science. When you get to Ideologies, you have a choice to make. Ignore Autocracy as that is not a Science-oriented choice. If you have 3-5 cities, Freedom is the best Ideology because Specialists require less food (Civil Society), and have reduced Unhappiness (Universal Suffrage). With a wide strategy (more than 5 cities) Order starts to look better. Getting Worker’s Faculties will give +25% Science from every Factory.
Exploration and Techs
Exploration is generally a good idea for a variety of reasons, but one to focus on here is the effect of meeting other players. In the first place, if you find other players who have researched techs you do not yet have, you can trade for them. You do this whenever possible. Remember, the other players will all be trading with each other anyway, so if you don’t participate you will simply fall behind. If you have a nice tech and can trade it to just two other players, you will jump up two techs along the tech tree, and that can be huge. If you hold onto it as a secret, some other player will research it, and they will trade it and get that boost instead. So trade whenever you can. Another advantage is that when you discover that another player has a tech you don’t have yet, your cost to research it goes down.
Trade
This is the next Science boost we will cover. when you set up a trade route with either another player or a City-State, one of the benefits can be an increase to your Science. The main benefit of trade routes is money, at least the way I play, so I will always start by looking for the best addition to my Treasury, but if I can choose between equivalent monetary rewards but one trade route offers more Science I might prefer that if I am going for a Science victory.
Choosing an Empire
There are many Empires you can play, and some of them are oriented to a Science victory. The two obvious choices are Babylon and Korea. Babylon gets a free Great Scientist when you discover Writing, which is very early, so you should use it to put down an Academy. And it earns Great Scientists 50% faster. Korea’s advantage comes from +2 Science from all specialists and from all Great Person tile improvements, plus you get a tech boost each time a Science building or wonder is built in the Capital. Of course, you can win a Science victory with any Empire if you are careful about leveraging your Empire’s strengths. For example, Venice and Portugal can rake in the gold in huge amounts, and you can buy a lot of stuff that way. Or with the Celts you generate a ton of Faith, and that can be used to buy buildings and Great Scientists with the right Social Policies.
Conclusion
This is just a quick overview of the Science path, and there is always more to learn. If you really want to dive into the Science options and get a Science Victory, the Civilization Fanatics site has a pretty good strategy guide at https://forums.civfanatics.com/threads/science-victory-guide-any-difficulty.530940/.