Hiya.
I jumped onto the forums because I specifically wanted some strategies to deal with this scenario. I generally am a bit of a girl with Civ, usually because I haven't the time to play the damn thing all the time to get better (a wife and 3 kids does make it harder).
But after a couple of frustrating (read: time wasting and wife annoying) attempts to get through it, I jumped on so I would have a better way to do this.
My strategy (with Rome) was as follows:
1. Get the cities in the north producing higher hammers, south to produce higher food. This will help later with building armies that traverse by sea.
2. All my beakers were for great engineers and I put them in the northern cities in the early part of the game.
3. Secured Silver and Fur. (settlers)
4. Built enough Praetorians to quickly declare war on the Celts. This was the reason for the engineers - to quickly get production ramped up and the Praetorian I's are enough to subdue the Celts. Knock off all cities on the continent, vassalise/ask for capitulation and then demand/trade for victory resource. This gets you on the board. I actually got the Celts pleased with me near the end of the game which was amazing. I was a good master to them and otherwise treated them fairly.
5. With enough engineers in the major producing cities, I started to specialise some cities producing Galleys and Triremes alternatively and some producing Praetorians and Trebs with a ratio of One treb for every two or three praets.
6. Once I had the cities pumping out units, I changed to the Upgrade Praetorians research and nabbed all those. With the odd exception as per below.
7. As units were being produced, I moved them via land and sea to the border of Greece's land. I also left a heavily guarded set of galleys with triremes near syracuse. Because I had (once they had enough population) been building culturally based buildings in the south of italy, it did help in that one square of sicily was mine, so I could unload all the units on the island.
8. Declared war on greece, invaded (modern day) greece, and grabbed syracuse. The victory resource is near athens. Once the main part of greece was conquered, sued for peace.
9. Switched research over to Great Artists. My brother (who doesn't play Civ), reckons using culture is a wimpy way, but it came in handy. Put a couple of great artists in Syracuse to build great work (+4000 culture immediately - to get culture up over 5000) and the same for the the cities in greece. Athens tends to try to revolt a lot, so reinforce it. The more you prevent it revolting and having the culture (therefore borders) over the victory resource, the less turns you lose without control over the victory resource.
10. By having increased culture in syracuse and Pisae, the city (I forgot what it was called) on corsica revolted and joined me, which saved valuable units from conquering it, and allowed me to Great Artist it and placed cultural pressure on Sardinia. After Pisae became a cultural hotspot, it and Rome got all Great Generals being military instructors or mil academy and spitting out a unit every turn or 2. By the latter parts of the game, the majority of my army was being built in these cities, purely because of the mammoth speed I could accumulate an army, put it on boats and then move them on.
11. At this point I made a mistake. It wasn't critical, but probably stopped me from conquering the Cathagenians completely. I tried to conquer Rhodes (only) because I assumed (incorrectly and probably because I was too lazy/stupid to bother checking) that by conquering rhodes I could get naval access to the eastern part of the Carthagenian empire. Because I was under prepared on the mainland for war with Greece, I wasted valuable time reinforcing the greek mainland and conquering greek cities. It did allow me to vassalise Greece, but was a waste of time. In hindsight, I should have left it all, slowly reinforced greece on the mainland and focussed my preparations for war with carthage. Because Eastern Italian cities had by this point built most/all buildings, they could produce Praetorias and Trebs, thus allowing the build up of forces in Greece to get faster and faster.
12. At this point I was spitting out great artists and had my culture slider up and my beakers down (I also had few problems with war weariness, and as time went on and I increased the culture slider, no war weariness at all). This worked for me, though there was no precedent in the help guides on the forums for this, it's just more the way I play in general. With the great artists, I sent them all over gaul/germany to the celtic cities I had originally conquered. I find also by being culturally dominant that other powers don't like to declare war. I move the GAs into southern/western gaul and this combined with workers building multiple road routes, I was able to have a land based access that was similar in moves to naval supply of units to the Iberian peninsula. Because (owing to my stupid war with greece) I had conquered Gaulic/Iberian Greek cities, I had access. If I was avoiding war with greece, I'd go through the celtic cities, given I have full use of their roads.
13. At the same time as point 12. I built up units on the border of Carthage's European cities, a massive naval fleet off the coast of Italy to first invade the islands (by that time, culture had delivered me all but one island city) and onto north africa. Two pronged attack (as heavily insinuated on the forums) was the plan. I also put several great artists on my fleets, so that once conquered, I could Build Great Works, that stopped the revolts and allowed me to gear up to build military buildings to supply the armies (almost like an amphibious assault and supply unit, but using Carthage's former cities). This is even more helpful when the cities are too small to allow you to crack the whip to get the buildings finished.
14. The second major mistake I made was putting all the units on the islands (I overkilled) and not splitting the fleet and sending units by boat towards Iberia. I had the units reinforcing by land, but I realised that by boat helps too, especially in getting them in one hit (like a blitzkrieg) on the land, rather than unit at a time.
15. Declared war on Carthage, invaded and conquered the islands, grabbed all the cities in the eastern half (with the exception of 2 that greece took, because in being my vassal, they were at war, and therefore took them. But like I said, vassalising Greece before conquering Carthage was a mistake, so you should be able to conquer all of Eastern North African Carthage). In Northern Africa, the purple victory point stronghold is near Carthage City. Again, massive GA reinforcement of carthage and nearby cities to avoid revolts robbing you of valuable points.
16 At the same time, conquered the Iberian Carthage cities, GA's in them. This was the point I realised that I needed my navy and units there quicker so I could then press on over Gibralter. Because I'd made the mistake with Greece and the navy and the war had started to get attritional, I got bogged down. Fine I was winning, but I didn't leave enough time to conquer Carthage. If I hadn't made the mistakes, I would have conquered Carthage because 1. I would have had the units on had to move onto Africa via the West (aka continue blitzkrieging) and 2. Had the time to conquer Carthage and then focus my energies on mopping up the remainder of Greece's empire.
17. Ideally, at this point (my game ended with 4 carthage cities unconquered and they still refused vassalage - probably an allusion to actual history), you would continue reinforcing the Eastern former Carthagenian cities from Italy and the Western half from the 2nd navy from Mediterranean Gaul, Italy+navy and the conquered cities. If I'd done it right, I would have wiped out Carthage using this method and used GA's and units to avoid revolts in the cities. I would then use the production power in Italy that I didn't need to quickly build enough units to overwhelm Greece's remaining cities and conquer completely (obviously I couldn't access their city in the middle east). My calcs are that with the time wasted with my mistakes, I would have had some time (and a massive amount of units) to have a crack at Egypt, though with their axeman, even having Praetoria VII's, I still would probably have struggled to do anything more than drive them from Turkey. But it would have given me something to do until the game finished.
18. all in all I enjoyed getting this one right, because I learned a lot and I enjoyed writing the "how to". Even with my mistakes, I was a bee's willy away from a land domination victory and because I would have (if I did it again) wiped out Carthage and Greece (as opposed to vassalising Greece and only receiving 50% land value for them), I think I could have achieved it, had I not made mistakes.