The new Ancient Med variant is based on the Diplomacy variant invented by Don Hessong. Don's rules can be found at http://www.variantbank.org/results/rules/a/ancient_med.htm, and these are the basic rules we are using here at PlayDiplomacy.
The rules are pretty clear, but it may be useful to have some specific points drawn out for added clarity.
1. The Nile
The Nile delta and Nile regions are covered in the referenced rules, but it can be a bit confusing to first-timers. Basically, what it means is you can travel from Alexandria to Memphis or Thebes, and then on to Bayuda. Also because of the delta and the river, it is worth resstressing that effectively Sinai and Thebes have single coastlines. In this game, there are NO TERRITORIES with multiple coasts. For every coastal territory, the coast is topologically one coast.
2. Balaeres
Is actually implemented on PlayDip as an 'Archipelago' - a mixture of an island and a sea space. Again, this is covered in the rules above, but it is worth restressing. An army cannot move to or from Bal without the help of a convoy, because it is an island. But it is also a sea square, and so a fleet sitting in Bal actually counts as being at Sea AS WELL as on the coast - in other words, it occupies the supply centre but can also be part of a convoy route. However note that it cannot be part of a convoy to Bal because that would put two units in one territory.
3. There are various 'land bridges' indicated on the map. These allow free movement by army or coastal fleet between Mauretania / Saguntum, Sicily / Naples, Corsica / Sardinia and Sparta / Athens. Note that the Sparta/Athens join also allows fleets to go through the 'canal', allowing a fleet to come from Aeg to Athens and on the next turn from Athens to Ion. But remember you can NOT go from Aeg to Ion in one go. Think the Kiel canal in the standard game. Also, Byzantium behaves in exactly the same way as Constantinople in the standard game.
4. The multi-arrows indicate movement possible in all the directions. So to be clear, for the Nile delta for example you can move Gulf of Pelusium - Thebes, GoP - Alex, GoP-Sinaii, Alex - Sinaii etc., and Messenian Sea can move to Gulf of Tacape, Ausonian Sea, Libyan Sea. Note that there is no blockage in the crossing point - so Mess can move to GoT at the same time as Aus moves to Lib Sea, and Alex can move Sinaii while GoP moves to Thebes.
Apart from these rule changes, the game will play with all the variants that the Classic game plays (FoW, Stuff, Chaos etc). The only one that does not work is Fleet Rome. Unlike the referenced rules, which suggest the game should start at AD 01, the PlayDiplomacy Ancient Med variant will start at 400BC.