Council Bluffs is essentially Omaha Eights-or-Better, only it's not played as a split pot game. The entire pot is either taken by the best low hand (if there's a qualifying Omaha low on the board), or the best high hand (if there isn't.)
As with Omaha and O8B, you deal four cards to each player, following by a round of betting. A three card flop is revealed, followed by a round of betting, then a single turn and river card are revealed, each followed by a round of betting.
Players then make their best five card hand using exactly two cards from their hand, and exactly three cards from the table.
If there are three different cards eight or lower on the board, 'best hand' then becomes the best low hand. Your best hand isn't determined by normal 'lowball' rules, though, as you must use three cards eight or lower from the board. The cards you use from your hand have no such restriction.
Example 1: Two players show down their hand at the end. The board is A-2-8-10-J, meaning the best low hand will take the pot. Player A shows A-2-Q-K; Player B shows 10-J-Q-K. Because both players must use the A-2-8 from the board, Player B will take the pot by using their 10-J; Player A, having been counterfeited on their A-2, must use their Q-K.
If there are not three different cards eight or lower on the board, however, the hand is played just as if it were regular high Omaha, and the best poker hand takes the pot.
Example 2: Same two players, same hole cards, but the board is now A-2-2-10-J. Player A and Player B now tie with ace-high straights (both using A-J-10 from the board, and K-Q from their hands) and chop the pot.
Strategically, it's quite different from either 'regular' version of Omaha (high or O8B). For example, consider the following:
Your hand: A-A-K-Q
The board: A-A-2-9.
Currently, you hold the absolute best possible high hand -- quad aces. If the river card makes a low, though, (24 outs to do so -- any card three through eight) your hand is dead. You'll be playing the worst possible low hand, using your K-Q.
That potential uncertainty as to whether the board will play high or low heading to the river is what makes the game so evil, and what makes its name (Council Bluffs being the smaller city in Iowa across the Missouri River from Omaha) so appropriate. The winner is often going to be the player who can make it 'across the river' with their hand intact.
One other strategic tip I've gleaned from the little that I've played the game so far: low pocket pairs are worth even less than they are in regular high Omaha, since even if you hit trips the odds are that much better the hand will be played for low, and your trips will be worthless.
Personally I think the game is brilliant. It fits nicely into the Omaha 'family' but is different enough to offer some very unique problems and opportunities, and it has at least as much 'heartbreak' potential as other forms of Omaha.