I'm going to take a brief moment to bask in the glory of that comment before giving an honest response. Ahhhhh...
Now, for the serious answer (understand that recent AI tweaks have greatly strengthened the AI's abilities overall in the game so this is seriously cool to hear):
There are numerous ways to go through the tech tree and some of the ways to get a good head start don't LOOK like the best paths to take because they may seem undervalued. One thing I do is to almost always put production first. If you can keep up/get ahead of building the effective buildings that get unlocked along the way you will be able to get the most in the smallest amount of time. However, I've noticed from the multiplayer games we have running that my focus on staying on top of accessed buildings may hold me back from actively expanding fast enough in the face of neighbors who will soak up the real estate before I can get out to it. However, my methods have proven to keep me ahead in technology and if that's your concern then follow my advice.
Make sure you strike forward to get your education levels nice and strong... but not too strong in the first few eras since there's a cap on how beneficial it can be that expands as eras advance. But right at the very beginning, making some choices to go for early education can make a very very very big difference, particularly the harder your game setting is.
Then head for the stone tools workshop and have your otherwise unnecessary storage pit built by the time you access the tech that provides the STW so that you can immediately begin building it while you research all of the techs that give a bonus (tech and production) to the Stone Tools Workshop. As soon as you have gotten all the ones that do that are within easy reach, then shoot for the Elder Council. You may be able to take a few detours to try and get your unhealth deficit eliminated along the way so that any food you get from hunting can actually accumulate towards city growth and not get wasted.
Then shoot for food food food.
Once you've soaked up all the quick and easy food benefit buildings and techs, then it's a little more dependent on whether you're on the coast or inland. But going back to developing the techs that give production benefiting buildings is usually the next step and at this point there's often quite a few.
From there you've gotta slog through a few not-so-beneficial techs but if you start shooting for Canine Domestication, Chiefdom, and on through to Sedentary Lifestyle, you may be able to hit Sedentary Lifestyle first and be the beneficiary of the free tech for doing so. However, going after a religion may be an objective along the way.
Anyhow, if you can figure out the best way to traverse the Prehistoric from these vague guidelines, you should be able to sort out some improved ways to get through Ancient and Classical, but I don't feel there's any perfect solutions in these eras as there's so many ways to go about it from reaching out deep into the tree to grab slightly more beneficial techs than others to simply grabbing at what seems to be able to answer the need you most face at the time. But in the Ancient, don't overlook the techs that could give you a wonder that can get you a free tech. There's a few of them to be had there and they can make a difference (but will often lead you far away from other more beneficial paths so it's quite cleverly designed to frustrate!)
Beyond that, you're on your own. However, I suggest being as well prepared to grow as you possibly can by the time you hit tribalism so you can immediately begin striking out to settle as soon as you're enabled to. That's been one of my own flaws in strategy I've been trying to improve on. (However, early overexpansion can easily choke off your economy and lead you to financial troubles which can lead to BIG research impediments.)
If you're problem is later in the game and you're trying to catch up... war war war war war. Capturing cities from more advanced players will give you a lot of free research towards numerous techs and will go a long ways towards helping you catch up. But you've gotta be very good at out-strategizing your opponent if you're getting out-teched.
