... Everyone here seems to have a specific build order of what to build, when to build it, and why. I look forward to your replies!
Everyone but me, it seems.
For you, i think the three most important things to know right now: food, happiness and production.
Food. You see, more food means faster growth, and faster growth means more everything in not so distant future, and from then on. Therefore, you need to get best +food things working for you - pick cities' locations with lots of good +food tiles and +food resources whenever possible, build most efficient +food wonders like Temple of Artemis, etc. This is more important to get than any +science, +production, +faith or +culture things, in my opinion. Prioritize +food things. For me, it goes as far as always building farms on river+hill tiles (and not mines), for example. And i find results extremely satisfying.
Happiness. If you'd follow the above and aim for as fast growth as possible, or close to it, then quite in many games you'd find yourself "hitting a wall" of not-enough-happiness. Too fast growth and too large empires - are limited by happiness level. Growth ceases if your empire is unhappy. For me, the way to handle happiness problems - is two-fold. 1st, i always plan ahead about building cities. It depends very much on map size (there are coefficients), but general wisdom is that for "tall" empires - i.e. few large cities - 4-5 cities on a normal-size map is the way to go. You see, if you'd build just 2 more cities, then quite likely you'd hit that "not enough happiness!" wall, real hard. On huge maps, it's about double that many cities before hitting that wall. With a few games, you'll get a feeling how many cities and how soon you'd want to create. It also depends on terrain (how many luxuries you get from your lands?), and on your trade relations (do you get many luxury resources from other civs and city-scates?). And of course, on difficulty level, too. Then, there are ways to "push" that "wall" further and further away, too: all the policies, wonders and buildings which give +happiness. That's the 2nd way to handle happiness problem - all these +happiness things. But, of course, you can't get all of them at once. They all are becoming available during various parts of the game, as you unlock technologies, build things, establish good relations with other civs. So it's kind of ongoing battle within your own empire - its growth vs its piling unhappiness. Master this process by being able to remain at fast or very fast growth - while being always able to remain at positive (not nesessarily large) happiness levels, - and you'll do quite good in any civ5 game, good enough to go Emperor difficulty (or even higher) with little or no problem.
Production. For most of the game, - all the way up to Information era, i'd say, if not through it, even, - this is your priority whereever you can't get any significant boosts to food or happiness. Or when you don't need extra happiness for quite a while, too. Production allows you to have more units, more buildings (and there are all sorts of buildings - giving you all kinds of good things), and more wonders (same thing as buildings). This is the base of your security, conquest and defense potential, of your cultural growth (the more things you can build, and the faster you can build them - the more culture you'll get from all those +culture things you build), your science and commerce (you build those things too), and your religion. Should you focus on any of those things before production - all the other things would suffer. And it's bad, because there are all sorts of reverse ties, most of which are weaker than "high production means more of nearly everything", - but piling up, those reverse ties are massive together. When i say "reverse ties", i mean +food, +production or +happiness boosts out of those "secondary" mechanics (which are, again, military might, culture, science, commerce and religion). Some of these "reverse ties" - are:
- strong military allows to fend off any attack and get any land you'd want - results in more food production (total made over any period of time) for your empire;
- higher +culture gives more and faster social policies - many of which are great +happiness boosters;
- the better your science is, the faster you'll get access to wonderful new buildings for +production, +happiness and +food (or +growth, like Medical Lab);
- the more gold per turn you have, the more things you can buy in case of emergency, for convinience, or to speed up your growth or production;
- the higher +faith you got, the more great people, religious buildings and units you can get - and through great people, you can get lots of +production with great engineers, for example.
Quite many people will disagree with me when i put science among "secondary" objectives in this game. However, it's all related to how much +food you are able to get, and how fast and big your +happiness gains are. At some point, if you're good enough with +food and +happiness, - you get lots of science AUTOMATIUCALLY, since all that population growth inevitably gives more and more +science (every citizen does some science. Every one). So it becomes quite literally impossible to "catch up" with that fast scientific progress - to build much (least all) of all new things any soon after they are made available by science. In other words, production "lags behind" when you focus on growth and large early +happiness gains. That's why i put production ahead of science. That said, yes, science is obviously the most important of all those "secondary" mechanics i designate. Cities near mountains (for observatories) is definitely one of my largest city-location priorities, for example.
All the above works quite well on moderate to a-bit-higher difficulty levels for all kinds of victories, and i think it's a good way to get familiar with the game and a good starting point to develop special strategies for specific victory types. Good luck!