I'm sure Moriarte has better perspective on this, he's better at Liberty Domination than I am for sure. But, here's how I generally play it. On Deity, the AI typically enters the Renaissance on or before t110. That's when you get your first spy.
If you play it right, you can use that first spy to get you Education, and build/rush-buy Universities on t120-125. If you're maximizing growth, happiness, and filling those specialist slots, you can get Artillery by t165 this way, bulbing Oxford to complete Dynamite. Possibly earlier, but I kinda suck at this.
If I'm going for Artillery, I enter the Industrial Era through Fertilizer to boost my growth. Chemistry is right before that, and the extra production will help you win the World's Fair.
Whether I detour to Engineering before Civil Service has a lot to do with whether I'm planning on continuing my conquest with XBows, and whether there's an available high-beaker trade route I want. Engineering pays for itself if you get that caravan out quickly. If I do go for XBows, I go for them before Civil Service usually, because timing is everything, and get them earlier if you go for machinery first.
So, the tech path has to do with how my game is going. If I have good tech momentum and my CB army is kicking ass, and I think I can hit XBows early enough AND can continue the conquest, which usually depends on terrain & diplomacy, then I go straight for Machinery, then Civil Service, steal Education and beeline Dynamite.
If things aren't going well though, I beeline Civil Service, Education, Sci Theory, and then go for Dynamite IF I'm doing well enough to hit Dynamite by t175 at the latest.
If you can't hit Dynamite by t175, you aren't going to capture more than maybe one or two capitals, and by skipping Sci Theory, you're delaying Biology/Flight/Combustion.
There are many branch points for me, each with a different estimated victory time that I'm pulling out of my ass:
1) Machinery->Philosophy->Civil Service->Dynamite->Flight. Victory on t210-t250, the goal being to either win with Artillery, or only have 1-2 opponents you have to kill with bombers. Steal Education and blow off public schools.
I do this if I have good tech momentum and promoted CBs, and I've knocked off at least 3 civs by the time XBow rush loses momentum. That leaves 4 civs to kill with Artillery. Splitting your army can accomplish this if terrain allows. If you lose momentum with Artillery, stop and go for Biology & Flight. I usually go for Flight first for the Ideology, but there's an argument for going for Biology first to ensure you have oil when you get Flight.
2) Education->Dynamite->Flight. Victory on t220-t250
I do this when I don't like the map for CB/XBow rush or if things just aren't going well. Like, if you CB rush successfully, but have no Trade Route beakers, or your empire has growth/happiness issues, or if geography makes an XBow Rush impractical, or if your CB rush fails.
3) Sci Theory->Dynamite->Flight. Victory on t220-t250.
If things just aren't going well from the beginning, just suck it up and go for Scientific Theory before Dynamite.
4) Machinery->Scientific Theory->Flight. Victory on t230-t250.
I typically do this if I think I can get some cities with XBows, but when I get to Machinery I can tell my tech is too far behind to hit Artillery at a reasonable time.
5) Education->Sci Theory->Flight->Combustion. Victory on t230-t260.
If things REALLY aren't going well throughout the game, Artillery rush is no longer an option, but the game is salvageable.
6) Plastics->Rocketry->Nanotech/Stealth. Victory on t250-t290.
If worst comes to worst, just keep focusing on science and cap most cities with Rocket Artillery, and finish off the rest with XCOM and Stealth Bombers.
Of course, I'm sure some will disagree. These are just estimates based on how my Domination games have gone.
EDIT: Oh, I forgot one more totally valid option:
Construction->Philosophy->Machinery->Civil Service->Dynamite. (or any variation after Construction->Philosophy)
This path is best if you're isolated IMHO. You need the NC as early as possible if you're not getting trade route beakers.
It also works great if you ARE getting good TR beakers and you want to start your conquest with XBows. (You'll get XBows at least ten turns earlier this way)
The problem with starting conquest with XBows is if they're not heavily promoted, XBow rush is MUCH less effective. Starting with CB Rush means you have Range AND Logistics when you get XBows, which is *everything*.
So, if you're going to start your rush with XBows, I recommend attacking a neighbor EARLY, and farming XP for your CBs while you tech Machinery. You want those promotions before you get Machinery.
For optimal farming, I recommend DoWing a CS too. 3 CBs on a CS and 3 CBs on a neighbor's city ensures that everyone gets XP every turn.
However, this is not a trivial task. It takes a LOT of practice to get good at farming XP without losing units. tommynt makes it sound easy, "stack xp, never lose a unit"... yeah, easy for him to say.