I have won religious victories a few times, before Winter patch though. Russia is the best for Religious Victory, imo. Though they are a bit worse after Winter patch.
For Russia strategy, get Dance of Aurora pantheon. Then get 2 Holy Sites (also scout to see if you can get 1 from capturing a city from your neighbor) which should be enough to get you as the 2nd-4th religion.
With Dance of Aurora and Russia unique ability and probably double HS's adjacency bonus policy card, you should have your first missionary ready soon. This should be enough to convert most of your core cities. Build a few more Lavras if possible and wait for your first few apostles. Use them to evangelize 2 more believes: "Mosque" and "Scripture or Holy Order" and if there is a competing religion around also start an Inquisition.
If you are lucky and there is no competing religion on your continent, it should be easy win. If not then start accumulating your Inquisitors until you have at least 3 of them, before you build more missionaries and apostles to spread your religion. These inquisitors will be your main defensive forces, keep them together in and around Holy Site and when enemy apostles and/or missionaries are passing by, you massacre them. You don't have to rush your Inquisitors to kill the enemies right away when they come in to convert your cities, if all of your cities have already converted to your religion. Let them use their valuable charges to convert a few of your cities first. Already converted cities are quite more difficult to convert to another religion, especially for city size 7 or bigger (size 13 city is almost impossible to convert, except for an apostle with Proselytizer or Translator ability), so the enemies should spend quite some charges and probably 1 or 2 apostles to convert a few of your cities and you can convert each city back easily with just 1 charge from your Inquisitor.
For spreading your religion, first you should consider whether that civ has found their own religion or not and you plan to invade that civ or not. If you plan to invade them, don't waste time to actively convert them. Just use Inquisitor to convert them after you have conquer their cities. If that civ has found a religion and have strong faith generation, you should seriously consider whether you can invade them and capture a few cities with Holy Site (or at least pillage some Holy Sites to slow them down) and also kill some of their religious units with your military units in the process.
For civs that you cannot or don't want to invade, if they did not found a religion, then send a missionary to scout first to see if there are some cities that don't convert to any religion left. If there are, then send more missionaries to convert them (the scout missionary should move just 1 tile each time when in enemy land, so if they see apostles they can hopefully withdraw back). If there is no unconverted city or you see some apostles, then withdraw back and build apostles until you have at least a few apostles with one of them has Proselytizer/Translator ability (keep building them until you get at least one with this ability). Move this offensive forces together (preferably with a missionary) and target a big city with Holy Site first if you have Proselytizer ability since it can convert almost any city with just 1 charge. If you only have Translator then target a medium city with Holy Site. Keep sending reinforcements (both apostles and missionaries) and withdraw them to heal in your territory if need arise. You should switch to buy apostle when missionary cost is more than half of apostle cost. You should use apostle charges just to change a city from another religion to neutral (the symbol of another religion disappear from that city and a pantheon symbol appear instead), then use missionary charge to convert it to your religion (because it is easier to convert nuetral city).
For civ that has found its own religion, you should wait for their apostles/missionaries horde to invade you first, then kill them with your Inquisitors to soften their force before you send yours to convert their cities. While you are waiting, you should build up more apostles to invade than in case of non-religion founders above. Preferably with apostle with Debate ability. Try to convert most (if not all) of their cities with Holy Sites in one fell swoop. Repeat the process civ by civ.
In case that there is another strong religious civ in another continent that you have a problem converting, consider invading it with your military to try to kill some of their apostles/Inquisitors with your troops. You should also bring some of your religious units to draw out their apostles/Inquisitors to the battlefield. You should at least be able to keep the invasion for sometimes and can kill some of its religious units, in case that you can't capture its cities. Because usually the strongest religious civ won't be that ahead in science and won't have that strong military either. So even though you lack behind a bit in some areas due to your focus on religion, you should be able to push this through.