Ah, Russia. The reason I have Peter as my avatar. Strong, flexible, easy for a beginner to play, and can win with any victory type. As much as I try to play every civ in this game, I'm always falling back onto this civ. They are very easy to learn but have many great, hidden talents that casual players might miss.
Civ Ability: Mother Russia
A great ability because you get it from Turn One. Having 8 extra tiles per city you found is not only a great way to acquire territory, but it makes it so much more flexible where you want to settle. You can settle on rivers while a resource is just out of arm's reach. It gives you options on what you want to work/improve with your workers. It's one of those things you get used to, and doesn't seem like much, once you switch to a Non-Russia civ, you notice the difference.
Production and faith on tundra is amazing. My favorite aspect of this ability. Tundra is already a pretty weak area of land. With these bonuses, it allows you to settle onto places other civs don't even consider. Extra production is always nice, but I think the Faith is the real winner here. If you settle your capital on tundra, you are generating +1 Faith from turn one. There is no need to wait to unlock God-King and wait an additional 25 turns to unlock a pantheon. Only Indonesia is faster at generating a pantheon. (Although Mali will give them all a run for their money but they're not out yet.) Couple this with Dance of the Aurora and you can get some insane faith generation going. Not only do your lavras get an adjacency bonus from surrounding tundra tiles from your pantheon, each tundra tile you are working generates an additional +1 faith. Amazing synergy.
Leader Ability: The Grand Embassy
This is one of the most underrated abilities in the game. It finished a very unceremoniously 3rd from last on the latest Leader Ability Elimination Thread. This is simply a free, reliable source of Science AND Culture throughout the game. Let's look at it close up:
Trade Routes to more advanced civilizations grant Russia +1 Science for every three technologies that civilization is ahead of them, and +1 Culture for every three civics.
First of all, many people think that "the weaker you are in science/culture, the stronger it is, therefore it punishes you if you're strong in science/culture". That's completely false. Notice how it says to more advance civilizations. You can be #2 in Science or Culture, and if you're sending trade routes to the leader, you're getting science/culture. This is especially helpful if you have runaways like Pericles or Korea in your game. You'll always want to send your trade routes to the science/culture leader, depending on which you prefer. You basically leech off them. It is easy to activate and reliable.
Second, the higher the difficulty, the better it is. Take Deity for example. I don't care how good you are, you WILL be behind science and culture for the first half of the game no matter what. This allows you to slingshot forward based on the powers that the AI is given in higher difficulty. Getting sources of Science AND Culture are extremely helpful on higher difficulties where every turn/decision counts.
Third, it is based on techonologies/civics NOT science/culture per turn. A huge difference. Hypothetically, you can have more Science AND Culture per turn than any other civ in the game, yet still get this ability to proc! The AI naturally fills in the trees. It doesn't beeline. Whereas, you can be generating a ridiculous amount of science/culture, and since you are Russia you will want to beeline anyways. Science, you want Military Science (Cossacks) ASAP. So get your basic stuff out of the way then head straight for that. Culture, you definitely need Theology and later Reformed Church. Russia is all about getting to your needed techs/civics as soon as you can. This is designed to help you with that.
Let's repeat: You can have the highest science per turn and culture per turn. You might even have unlocked techs before others. As long as you're sending trade routes to civs with the most techs/civs, you will get science/culture out of them. It is extremely easy to use and abuse.
Unique Unit: Cossack
Don't let the defensive bias fool you. You can still take these guys on the warpath for domination victories. Obviously they have bonuses to fighting in their own territory (and imagine how much stronger they are with Defender of the Faith). So they are wonderful at defense. Once you get them, you are free to pursue a Religious, Scientific, or Cutural victory without any more military threats. I've had many deity games as Russia where I'm getting my ass kicked prior to these guys coming online, and once I get them, I'm able to push back and then set into motion my victory. I'll explain more about domination with them further below.
Unique Infrastructure: Lavra
This came in second for the Unique Infrastructure Elimination Thread. It's that powerful. A half-price holy site which gives +2 Great Prophet Points and +1 each for GWAMs. Half-price means you can build it in small cities in the tundra. And it comes online sooner. The extra Great Prophet Point means not only are you getting early choice of pantheon with the Civ Ability, but you get early choice of religion as well. Finally, you get +1 Great Writer, +1 Great Artist, and +1 Great Musician point per turn. This makes cultural victory from collecting GWAMs a reality. In fact, one complaint people have about Russia is that you will generate so many GWAMs you will run out of places to store their works. It happens. And that's a First World Problem if there ever is one.
Now, what I especially love about Russia is their flexibility. They are known primarily as the best Religious civ, with a very strong secondary focus on Cultural victories, but I think they can do quite well in Domination and Scientific victories as well. They key to all that is their unrivaled faith output and using faith as a currency to whatever you need.
Religious Victory
The most straightforward and easiest for a beginner to understand. Get Dance of the Aurora. Settle as much as you can in tundra and build as many lavras as possible. Even if it's a small Size 3 town with no water source, you want a lavra. Start thinking of your towns as just glorified lavras. Between your Civ Ability and Dance, your faith generation will skyrocket. Use that to buy apostles and missionaries. You can simply beat other civs out of attrition, because they can't match you. Good beliefs to get are Choral Music or Feed the World. Choral Music makes sense because you will be building shrines/temples in all your cities so that's a deep source of culture you can use. Feed the World for the same reason, but for growth. You can't build farms on tundra, so your ability to grow will hurt. Ultimately, I think Choral Music is the better choice, but you should really play with both to see what you prefer. You will want Mosques for that extra +1 spread. Makes each missionary/apostle go further. Finally, Defender of the Faith, Holy Order, or Missionary Zeal will do. Your faith output as Russia can be so strong that Holy Order (30% cheaper apostles) is pointless. Having Defender of the Faith might be better as it makes it easier to defend your territory with a smaller army. Missionary Zeal allows you to spread so much quicker, and when it comes to RV, the quicker the better.
Cultural Victory
You're going to want Lavras and Theatre Squares everywhere. You'll be generating so many Great People, but you need a place to house them. Pick Jesuit Education for a religious belief so you can leverage all that faith into insta-buying Amphitheatres and Art Museums. Definitely pick Cathedrals. You will have a monopoly on Religious Art, so you will have a place to put them. Also look at getting some naturalists. Tundra is high appeal territory. You can easily make a national park or two in your empire since you're going to be expanded all across the tundra, and each of your cities start off with 8 tiles.
Domination Victory
This is a very late start. So you're not going to be unleashing War Carts in the Ancient, or Heteroi in the Classical, or a Mongol Horde in the Medieval. You have to wait until Industrial. But if the idea of turtling for the first half of the game and then unleashing your army upon the world sounds exciting, read on. Cossacks come online at Military Science. It's what you will want to beeline. Going Dom route, you'll definitely want some campuses in your cities. When doing Religious, I just ignore them, but we're doing it differently. Get to Military Science ASAP. Fortunately, on the civics tree, the ability to form Corps come around the same time. So ideally, you don't want to just produce Cossacks, but Cossack Corps. They hit at 77 base, and if you use Crusade, you can get them attacking cities at 87. In the early Industrial Era.
So yeah, obviously religion-wise you will want to pick Crusade. Use your faith to convert the cities you want to target. You'll especially want to go Theocracy + Grandmaster's Chapel. And then choose the Raid policy card. Cossacks are able to pillage then attack. It gives them amazing versatility. You'll want to pillage your enemies as much as possible. Say you land on an fully-upgraded enemy campus. You get 50 science from pillaging the campus, 50 for the library, 50 for the university, and 50 from the research lab. That's 200 science in a single turn. But you still get 30 faith per pillage so 30 x 4 = 120 faith on top of that. Use that faith to buy more missionaries to target other cities, or faith-buy additional cossack corps.
Science Victory
This is probably their weakest victory type, but they aren't weak at it at all! With Rise and Fall, they can be quite good at this. So, it's a bit of an unorthodox route to get to Mars because you use the orthodox faith to get there. Instead of just going for campuses and such right away like any other civ for science victories, you want lavras. You'll need them in every city you have. You will also need commercial hubs and/or harbors so you can have trade routes. Religiously aim for Wats so you can get +2 science in every city, and for Stewardship which gives you more science the more your religion spreads. Jesuit Education so you can instantly buy libraries and universities. Saves production, and they can start generating Science immediately without having to wait. Trade Routes in every city and send it to whomever has the highest science. Get as many cities with as many lavras as possible. Then go into a Dark Age and select the Monasticism policy card: 75% Science for every city with a holy site (AKA all your cities now generate 75% more science!). They can be quite similar with Arabia in this regard as this a religion-infused scientific victory which Arabia is excels at, but they can hold their own this way as well.