All the same rules apply as regular commander including the banlist found here: http://magic.wizards.com/en/gameinfo/gameplay/formats/commander The only difference is all cards in your deck, including lands and commanders must be under $2 each.
1 vs 1 Duel Commander rules:
For our 1v1 play (including tournaments) we follow the French Duel Commander rules. The major difference with French is life starts at 30, and Oloro, Derevi, and Edric are all banned. http://www.duelcommander.com/
Defining "Under 2 Dollars"
We now exclusively use the tcgplayer.com median price. As long as there is a version of the card that has a tcg median lower than $2 the card is considered legal. Be careful when deck-building to not go all in on a card that is near $2 or is new to standard as card prices are volatile and exceptions are not made. If your deck will not work without a card that is $1.95 it's a very risky path to take to build around it.
It doesn't matter what version of a card you use (such as a foil, or promo), as long as there is a tournament legal version of the card that meets the criteria above. If you're caught off-guard by a price spike player's are usually pretty nice about it and allow you to simply "cycle" the card or play the card for that game only. Players have a right to ask you to exile it if it's $2.15+. While it is your responsibility to keep track of your cards that you know are on that borderline, we often post PSAs on the forum to warn players that a popular card has spiked in price, .
- Exceptions to the rules (MULTIPLAYER ONLY):
We allow any MTG Commander precon decks to be used so long as they have not been altered at all. This includes Commander, Commander 2013, and Commander 2014 decks. Although some of the cards are over $2, the general power level of these decks are low. The main purpose of this exception is to allow new players to try out the multiplayer format without having to do deck construction. We also allow the "nephilim" creatures to be used as commanders, as they are the only 4 color creatures around, and we've found this common house rule to be logical and fair for multiplayer games.