This strategy is basically an exploit of unbalanced game mechanics. If you get all parts of it together - and that is not too hard even on the highest difficulty levels in Single Player - you will be at a big advantage whatever your game might look like. All-in-all the strategy works well even if you miss on the 2-3 wonders you´re especially interested in.

Be aware that there is a bug increasing Persian Golden Ages to ridiculous numbers. This strategy is not based on this bug - depending on the settings and game plan, you´ll be in Golden Age most of the game bug or not.

In Civ5 tile yields have been generally decreased compared to Civ4, while Golden Ages still provide one additional production and gold to every tile that already generates either. Furthermore Golden Ages are much easier accessible: Excess happiness leads to it, Cultural Policies can trigger one, there is Taj Mahal and most importantly Great People including Great Generals can launch it. Finally GAs last slightly longer by default than in Civ4.

Basically Golden Ages are stronger by default, yet easier accessible than in Civ4. Enter Persia:

Persia´s Golden Ages last longer and provide a unit movement and combat bonus. The increased length is especially important, because each Golden Age lasts a turn shorter than the one before it down to three turns. The movement bonus is at least borderline overpowered as well. Together with the combat bonus waging war becomes very easy - but it´s also crucial for empire buildup transforming Persia´s workers into Indian Fast Worker from Civ4.

Golden Ages effectively fight the lack of production Civ5 brings with it (in relation to production costs), allow to ignore Trading Posts for a long time (until you got so many resources that setting up one or two gold cities is quickly and easily done) and for Persia they support both waging war or continuing buildup. The synergy of bonuses for waging war and Great Generals being able to continue Golden Ages is powerful as well.

You want to work as many tiles as possible to take advantage of the bonuses of the GAs, especially of the production bonus. Rivered Plains tiles are good (in GA 2food-2production-2gold), lumbermills on forests, rivered (1-3-2) or not (1-3) are great, so be careful about chopping away too much of those early on. Also your cities won´t be growing "too" big (=stay at relatatively low population) because you´ll rather will want to work production tiles which on average don´t provide too much food - e.g. not cutting forests to build lumbermills.

This means, expand fast, though don´t plant cities too far apart, instead claim as many tiles as possible. Depending on difficulty level and luxury resources aim for around 6-8 cities till turn 50 (quick speed). Generally keep on expanding as much as your happiness situation allows - build Colloseums early and in many cities. There is no need to go far beyond pop 4-5 in Civ5, rather just spam cities close and everywhere. Not only does this result in more production overall, but it especially helps controlling happiness much easier.

The more tiles your cities will work, the more you will take advantage of the fact that you´re in a Golden Age most of the game - also if you expand quickly neglecting worker construction a bit, the Golden Age with its additional movement point also for workers will help in getting all the cities running.

While getting an empire to make use of those Golden Ages, you also want to to attempt increasing their length further by going for Chitzen Itza and making sure in the first place you are able to trigger them.

Prevent Premature Happinization
If you play on lower game difficulty in Single Player or if it´s a MP game (Warlord/Prince difficulty) be careful not to launch your first GA through excess happiness too early, you want to be able to profit from it properly first. To "counter" the increased free happiness expand fast to a couple of cities and potentially don`t hook a happiness resource right away.

Great Library Sling Shot
The - already very popular - Civil Service bulb off of Great Library is especially powerful in this strategy. You get more food from farms on rivered tiles, which supports GP making and you get Chitzen Itza for sure, which is the main benefit since it increases the length of your Golden Ages further, not only making each one better, but also allowing for more (efficient ones) overall.

GP City
Great People are your main means of launching Golden Ages. Sadly different Specialists (and GP points from wonders) add to different GP pools in Civ5, decreasing overall GP output and spawn speed.

Within your first 3-5 cities you should select one which has some means of production, but mainly lots of food tiles. Especially (farmed) rivered tiles work well once you´ve gotten Civil Service. In most cases the GP city should be next to a river (more food from farms with Civil Service; requirement for water mills) and if possible a mountain (requirement for observatories).

Specialize the city heavily, only constructing buildings that either incease the food output of the city (e.g. granary, water mill) or help in spawning Great People. The GPs of choice are Great Scientists. Scientist Specialists will increase your research speed significantly - that and the fact that the city will be above average in size anyway has good synergy with the bonuses on research you get from Library -> University -> Public School, all of which are needed anyway in order to be able to use Scientist Specialists.

Develop the city cyclically. Grow it, switch to production tiles when getting a specialist enabling building, then grow again. Granaries and Water Mills can be build in between, not necessarily being rushed. If possible get the National Epic for the +25% bonus on GP making, but remember the restriction that you require a monument in each city to build it. Same for the National College with libraries.

Porcelain Tower / Taj Mahal
Those start a Golden Age, if you have the resources to spare, get ´em.

The Great Scientist you get for free can start a Golden Age - and it does so when you want it to. If for some reason you manage to get the Tower into your GP city, you can make full use of the 2 Great Scientist points as well. It requires a bigger commitment since Education often isn´t a prime target in the technology tree. The Tower is clearly much stronger than Taj Mahal since it´s much cheaper, yet can give the same benefit next to other since the GS can bulb a technology or build an Academy as well and it even provides the better GP points since GS are much more useful than GA in Civ5.

Taj Mahal is a much worse Porcelain Tower - it doesn´t do anything the Tower does, yet costs much more. With Persia (and/or) Chitzen Itza the Taj is still worth the hassle most of the time, especially since it comes at a point in the game where you should be having quite a few cities already, being able to use one to construct this expensive wonder.

Cultural Policies
Make use of the Piety Branch from the beginning, Philosophy being your "Classical Era trigger" most of the time, though should you lose Great Library, Construction works as well since you will want both lumbermills for big Golden Age production from forests and Colloseums for additional happiness anyway.

Pick Organized Religion to get your second "Excess Happiness Golden Age" quicker, folllowed by Mandate of Heaven/Reformation and then Free Religion.

What you do later on in the game depends on your general game plan. If I haven´t gone for conquest, but rather space race I like Rationalism -> Secularism -> Free Thought -> Scientific Revolution launched off of the 2 free Social Policies from Free Religion. Do that, work an average of 2 scientists per city, get 1-2 Trading Post cities (even though you don´t need them to stay in positive income) and watch your empire go off. Remember the bug that even though it says "Trading Posts +2 science" for Free Thought, it´s in fact just +1 science.

It all depends on your game plan. Besides a Cultural Victory you can do anything with this strategy. You can easily conquer everyone with your superior production, gold income, movement and combat bonus and good research. You can go for a space race for the same reason. You can even befriend City States since you´ll be having tons of money due to Golden Ages basically doubling your empire´s gold output.

The trickier part is the the earlier phase of the game (till around turns 70-80 on quick speed). Against the AI you shouldn´t be having much trouble here, a human might interfere more though... There though your general game plan will likely be less extensive anyway. You don´t need an infinite Golden Age, 2 or so dozen turns should do the trick here.

Just make sure you have enough cities while keeping on expanding throughout the entire game in order to take advantage of all those Golden Ages. If you launch an infinite GA with three or four cities, all the wonder/GP hassle won´t be worth it. Use the first to support your buildup past three cities and to get the great Library and the second one to initiate another buildup phase including Chitzen Itza.

If you´ve gotten Chitzen Itza having 6-8 cities and don´t die soon after, it´s basically Golden Age till the game is won.