There is no exact formula for start strategy, you just need to prioritize the first three points from the 4x abbreviation: explore, expand, exploit.
Prioritize scouting, growing your capital to 3-4 population before starting to build settlers so you can plant cities in good spots, working the best tiles and improving those tiles and other resource tiles. Train enough military to hold of barbs and any other threats, but don't exaggerate on early military since early hammers are very important. There are of course rushing strategies, when you want to built a massive military early, so there are variations according to situation.
Since in civ 5 science is so important, you want to prioritize growth and NC. Later on prioritize civil service for extra food, and Education. Build universities and work the slots ASAP. A good strategy for a fast NC is to get to 3-4 cities fast, maybe rush buy a library in the last one, and time building libraries with getting Philosophy so you can start on it right away.
A good build order for the initial game in the expo's would be granary (so you can both grow, and send food cargo) and library (sometimes you can switch, if you don't need the granary that fast).
In the capital usually it's not optimal to build a granary before settlers, since that delays settling your other cities, and does not really help when building settlers since growth is stagnated (it may add some hammers, but that usually does not make up for delaying the settling of expo's). After settlers you can build granary for growth, and then other stuff like caravans and units. You don't really need to rush library, just time it so you finish it when expos finish it.
Any Build Order no matter how good it is, is not set in stone. For example there is no point in building a Shrine if you don't want a religion and don't have a good pantheon that can really help you accelerate your start. Sometimes you need one scout, sometimes you need two or more. Sometimes you cans skip a monument and get one from Tradition, so you can start on your settlers faster. Sometimes you don't get to steal workers so you need to add workers to the Build Order, etc.
I would advise that in general building early wonders is a bad idea, especially Great Library, since it is very hard to get on greater difficulties, and you should be focusing on expanding at that point. On the long run this will give you more benefits. Of course there are some specific strategies that include an early wonder like Temple of Artemis, Pyramids, or others.
The tech order in the early game can vary from game to game very much. Since you need all the ancient era techs, you need to time them, and get them when you need them. Don't go for writing first if you don't need/have the time to build libraries soon, get other techs that help you now.
Prioritize techs that help with tile improvements (for example there is no sense rushing calendar if you don't have calendar resources). Techs that reveal strategic resources are also very important, because they help you make better decisions when settling, and give you extra hammers early game, which are very valuable.
Regarding your military, your initial warrior should come back and protect your tiles and workers after some basic scouting. The scout(s) should continue the scouting. Don't attack barb units early, especially with melee units, since you will most likely put yourself in bad positions. If there are lots of barbs get some archers to defend. Don't take the barb camps right away. Other barb camps will spawn because there is plenty of land that is not visible. Sometimes barbs will capture the AIs settlers so this will delay them and leave the area open for settling. Later on those barb camps may give you valuable stuff like influence with city states and/or free workers.
There are of course many more tips/tricks but usually good prioritizing and timing events is the best strategy, no matter how general it may sound.