For a good and detailed discussion of this crusade, please consult Barbara Tuchman's A Distant Mirror.  

The major crusader strategy was to besiege Mahdia.  The city was on a peninsula, and the crusaders camped across the neck of the peninsula.  They also planned to blockade the city by sea.

The Muslim strategy was to hold the city while harassing the crusaders with a relief army.  Anticipating the siege, the city had laid in ample supplies.  This helped in holding the city.  The relief army did not offer pitched battle to the crusaders.  Instead, the relied on light cavalry to make quick raids on the crusaders.  The crusaders suffered in their heavy armor in the hot sun and the Muslims did not allow them to get close enough to take advantage of that armor.  

As winter approached, the crusaders made one attempt to storm the city.  But the did not have enough siege weapons and the attempt failed.  The two sides then compromised and made peace.

The strategy and tactics then were siege on the part of the crusaders and harassing skirmishes on the part of the defenders to weaken the crusaders until they gave up.