I think that in general, the thread is underestimating the importance of tribal politics. In particular, you're not going to be appointed emperor unless you can make a compelling case that you're a Roman citizen (a bastard, presumably, since there aren't any records). If you're too black or too blonde or too female to pull that off, you're going to have to win by conquest (see below) or play power-behind-the-throne.
Assuming you have the right looks, I think you want to slow-play it: build up a fortune in business, get adopted by one of the elite families (not the Julians!), marry into another of the elite families (still not the Julians), and transition into a career of able public service. A generalship would be ideal, if you can swing it. At that point I see two options:
"Holy shit, Fezziwig, you're saying it'll take thirty years minimum?" Sadly, yes. It's tempting to try to sidestep Tiberius entirely and become Augustus' successor, but I don't buy it. Augustus and the senate won't accept you unless you're over 50 (or so) and have a proven record in governing stuff, and there's just not time to get that together before Gaius dies in 4AD and Tiberius gets officially tapped as successor.
So if you're impatient (or black, female, &c), you have to conquer Rome. That sounds harder than it is; all you need is (1) a group of people who'll let you lead them against Rome, and (2) a military advantage that's better than the tactics and discipline of the Roman legions. I had a strategy for generating (2), but Logos01 describes a better one, so let's go with that.
(1) is tricky. You need to be allowed to amass a military power base, so thoroughly Romanized provinces are out. You need access to a functioning economy to get your raw materials, so semi-nomadic herders like the Germans are out. You need a vaguely reasonable logistical chain, so Mexico and China are out. You need a state that actually wants a fight with Rome, so the Persians and the British are out.
If you have a solid ethnic in with the Egyptians or Jews, they're good choices: nominally Roman, but with a proud history of self-rule that should help you through the early delicate period where one informer ends the whole game. Failing that, I think your best option is a slave revolt: amass wealth, buy into one of the slave colonies, and recruit from there. You'll have to do the metallurgy yourself, at least at first, but at least your forces are hard to bribe.
Even with a military power-base, you probably want to wait until late Tiberius or middle Caligula, just so that the empire doesn't turn on you or fragment the instant you seize power. I guess you technically win if a rump session of the Senate coronates you while Rome burns outside, but it feels like we should award points for a smooth transition of power.
If you have a solid ethnic in with the Egyptians or Jews
Physical appearance isn't the whole story-- cultures change, and I'm not sure how hard it would be for a modern person, even with the appropriate appearance, to be accepted solidly as an insider.
A recent discussion post has compared the difficulty of an AI destroying modern human civilization to that of a modern human taking over the Roman Empire, with the implication that it is impossible.
The analogy has a few problems: first, modern humans don't have much greater raw intelligence than the Romans, only a bit more knowledge and tools; an AI would have a genuine intelligence advantage. Second, a high-tech civilization like ours offers many more ways for a genius to cause chaos than existed in classical Rome: it's more plausible that you can throw a few existing technologies together to create a superweapon than that Ptolemy could have done likewise, and there's no ancient Roman equivalent to hacking a nuclear launch system.
But taking over ancient Rome might serve as an interesting upper bound on the difficulty of an AI taking over modern civilization. And it's a theme of Harry Potter and the Methods of Rationality that rationalists should be able to come up with creative solutions to seemingly hard problems. So if Professor Quirrell offered it as an extra credit assignment, how would you take over Rome?
Here are the rules:
- You are thrown back in time to the year 1 AD. You can choose to arrive anywhere in the world, but your method of arrival cannot itself give an advantage (you can't appear in a flash of light in the middle of a religious ritual or anything).
- You do not start with Roman citizenship or any other legal record of your existence.
- You keep your original physical characteristics, including sex, height, and fitness. You will appear in period-appropriate dress of your choosing, and can't carry any artifacts with you. You may start with enough money to live a patrician lifestyle for a year.
- You are intellectually near-perfect. You know all human knowledge as of 2012. You speak fluent Latin (and all other languages of the day) and can orate as eloquently as Cicero or Demosthenes. You are a tactical genius of the order of Caesar and Napoleon. And you have infinite willpower and goal-directedness: aside from human necessities like sleep or food, you need never rest.
- You win if you either become Roman Emperor (and are acknowledged as such by most Romans), or if a state you control conquers the city of Rome. You lose if you die, of old age or otherwise, before completing either goal.