If you are just starting to try out on Sid, you may quickly notice that establishing a beachhead on Sid is really no picnic. By using an army to protect our landing parties, we can land safely without any problem. However, once we take over one of their cities or build a town on their continent, they will attack us with everything they get. In most case, they will out run our position without much of a problem. By using the following trick, I have been very successful with establishing a foothold on the AIs continent:
1. Going to war as usual, but do not send troops to their continent just yet. We want to surprise them as much as we can.
2. Find a good landing spot, referably next to their luxury or valuable resource. Our main goal is to take control of their resource since resource is very rare on Sid.
3. Assemble an invading force consisting with at least 1 settler, 1 army at full health, and enough troops to take out at least 2 of their cities. Have them standing ready but do not land just yet. Note: The AIs are usually defending their town with about 4 of their best defenders at this level.
4. Now we wait until the AI willing to accept our envoy.
5. Land our troops and attack with eveything we have. Note: our army will protect our troops during the landing turn. Raze all the surrounding cities as many as we can, then use our settler to build a town next to their luxuries/resources.
6. Immediately sign a peace treaty! We now have at least a few more more turns to fortify our beachhead. In most case, the AIs would give us the next 20 turns in peace, but I usually try to fortify my beachhead ASAP - never known when they might change their minds. Next, ship over a lot of cannons/artilleries and join workers to turn the little town turn it into a city to gain defensive bonus. Rushing the barracks is usually the first order of the day, then CivDefense if I the technology is available. Now the beachhead is pretty much secured.
7. At this point, I would like to recommend you to read SirPleb's guide to the Funnel of Doom next. It wouldn't hurt to prepare the Funnel of Doom to give extra protection for our beachhead (just in case).
1. Going to war as usual, but do not send troops to their continent just yet. We want to surprise them as much as we can.
2. Find a good landing spot, referably next to their luxury or valuable resource. Our main goal is to take control of their resource since resource is very rare on Sid.
3. Assemble an invading force consisting with at least 1 settler, 1 army at full health, and enough troops to take out at least 2 of their cities. Have them standing ready but do not land just yet. Note: The AIs are usually defending their town with about 4 of their best defenders at this level.
4. Now we wait until the AI willing to accept our envoy.
5. Land our troops and attack with eveything we have. Note: our army will protect our troops during the landing turn. Raze all the surrounding cities as many as we can, then use our settler to build a town next to their luxuries/resources.
6. Immediately sign a peace treaty! We now have at least a few more more turns to fortify our beachhead. In most case, the AIs would give us the next 20 turns in peace, but I usually try to fortify my beachhead ASAP - never known when they might change their minds. Next, ship over a lot of cannons/artilleries and join workers to turn the little town turn it into a city to gain defensive bonus. Rushing the barracks is usually the first order of the day, then CivDefense if I the technology is available. Now the beachhead is pretty much secured.

7. At this point, I would like to recommend you to read SirPleb's guide to the Funnel of Doom next. It wouldn't hurt to prepare the Funnel of Doom to give extra protection for our beachhead (just in case).

) and they'll never attack
Combining that with rushing army, it's not too hard to come up with at least 40 armies for the final showdown.
I was expanding so fast and running out of settler, so I had to use a non citizen settler to claim the land. About 40 turns later, for some strange reason, 1 peaceful Greek citizen was able to convince 7 of my Mayans to switch side (and I wasn't even at war with Greece). I was thinking of taking it right back, but decide to see if I can flip it back. Btw, Prothoe was defended by only 1 infantry. I hope it won't flip, but it's only wine.