Hey,
I read most of the answers and I just wanted to give my input. As a bit of background, I will tell you that I've played around 200-250h, and I've recently started winning on Deity. All victories at higher difficulties have been thru Science, since it's my play style at the moment. The only reason I climbed up was because I started watching Marbozir -a youtuber with multiple lets play Civ V deity (although there are multiple others, like Acken, moriarte, peddroelm...) with a very insightful commentary that will enhance your knowledge of the game instantly. However, I understand that you may not enjoy watching as much as playing, thus here are few tips (some may be very obvious):
-You could try to get a mountain in the capital.
-Scout early to find other Civs. Meeting them will reduce the cost of technologies already discovered by the AI (especially important at higher difficulties).
-Go tradition with 3-4 cities. Cities with mountain (+river) are great for science due to observatory.
-Build Libraries ASAP to get your national college (often together with aristocracy for the production bonus). Skip early game wonders (they are hard to build in higher difficulties).
-Keep your trades up, they are great for both money and science (cargos preferable).
-Beeline education. But workshops are really important too. Try to spam research agreements.
-Scientific Revolution, Plastics... Get Unis, Public Schools and Research labs asap (but don't be afraid to delay them for few turns if necessary).
-Get Rationalism ASAP and try to unlock scientific revolution (I believe is the last one on the left corner).
-Porcelain tower+ Scientific revolution is an awesome boost for your research agreements. This wonder is quite easy to build even at higher difficulties.
-Try to get high population using internal trade routes, being allied to maritime city states and having good food tiles. This will allow you to unlock multiple specialist as well as keeping your science output high.
-Never forget to maintain your army at a certain standard. If you don't have any aggressive neighbours you should be OK with a couple archers early. I find range units with a couple non-range to be OK. I often find myself trying to build building and neglecting this aspect. You should not be afraid to build units (especially with barracks and armoury) and stop your progress towards buildings (with moderation).
-Brive your neighbours to fight each other. This will keep them off your back and will reduce their strength.
-Once you are comfortable, I find myself at this position when I get Dynamite, you can try to invade your neighbour (especially, if he has many wonders)and increase your strength in other areas.
-Once you get the lead, just keep spamming research agreements and keep your army fit for a possible invasion. Try to get the scientific wonders- Hubble- as well as other late wonders (Neuschwanstein, Eiffel Tower...)
Others:
-Micromanagement of the city.
-About great scientist. I like to use them for academy until there are 60-80 turns remaining (in standard) or around modern era.
-Try to maximise the usage of free techs given by wonders like Oxford University or Rationalism finisher to sling-shot. E.g. OU to go from industrial to modern era and get quick ideology.
I guess I'm forgetting many other details. I hope it helps