I always was a little confused with the rebel fleet's strategy in that battkle.
If you have not already, pick up the novelization. It expands on things a bit. (It's also a good read.) C3PX covered the strategic side of things pretty well, what follows is pretty much my own impression from the films and EU, combined with a little invention.
The battle was not so much a hasty defense of Yavin, as it was an attempt to take out a high value target. The Alliance command cell with which the Organa family was associated, as we learned in ESB, was highly mobile and capable of dismantling and moving even top echelon command posts in a matter of hours. I wouldn't be surprised if most of the Rebel leaders had evacuated Yavin before the Death Star even arrived, leaving only a skeleton crew to take out the fighters. (Some sources indicate the Death Star arrived the day after the Falcon, giving Dodonna's staff time to analyze the DS plans while, perhaps, the rest of the leadership disappeared into the highly-dispersed fleet.)
Strategically, of course, the destruction or survival of the Death Star would shape the Rebellion's diplomatic, informational, military, and economic efforts throughout the galaxy. Its destruction was paramount if the Rebellion was going to succeed. If it had been allowed to run loose, the Rebels must have feared, Palpatine would have thrown off the last vestiges of benevolence--and the Rebels would have seen the dissolution of the Senate as a precursor to this--and revealed himself as the tyrant he was. Without the Death Star, the Empire had been forced to put on a friendly face in many of its dealings with its subjects. But with a Death Star, it would not need to. And as the galaxy came to know of the Death Star's atrocities, it would not be able to maintain that facade. Without the facade of civility, the Empire would rapidly devolve into utter brutality.
Operationally, the Rebels were probably limited by time and an imperfect command structure. A cell-based organization, pieced together from disparate resistance groups and dispersed throughout the galaxy, cannot possibly concentrate a large amount of combat power at one location based on a plan conceived by a handful of officers, overnight. So the only fighters and ships available to Dodonna would have been those under his headquarters. The capital ships would have been useless against the Death Star, and were probably used in the evacuation of the base. That leaves a few squads of X-wings and Y-wings.
Tactically, of course, we all know what happened. One group attempted to "draw their fire," probably by attacking soft targets of opportunity like hangars. The other group went into the longitudinal trench that led to the exhaust port. When the latter had been nearly destroyed, Luke was given command of a small group to make the last attack run. I understand why a green pilot like Luke was not on the first string, but why was he put in charge of Biggs, an Academy graduate, and Wedge, who had been in space most of his life? There's probably an interesting story there.
Anyway, Luke's group was forced to go in. Flying above the surface of the DS, they would have been in range of a great many guns. Flying through the trench, they only had to worry about one tower, apparently mounted just beyond the exhaust port. The trench would have confined their flight profile to almost a straight line, but they would be flying in a straight line anyway, to let the targeting computer lock on to the exhaust port. (Star Wars was written before things like laser-guided munitions were commonplace, so this scenario seems kind of odd today, but work with it.) Luke directed his flight to transit the trench at full throttle, hoping to put distance between themselves and the TIEs. In deep space a few kilometers wouldn't have mattered, but the jamming fields over the Death Star made a shot of even a few klicks difficult.
The remaining Rebel fighters were slowly picked off. Biggs was killed, and Wedge took damage to his fighter's engines. When he reported to Luke that he couldn't match Luke's speed, Luke ordered him to leave. (Remember that the Death Star's surface is curved, requiring constant acceleration to maintain the same speed and altitude.) When Luke's fighter was hit, it should've all been over. The Rebels' plan had failed. But the unplanned arrival of the Millennium Falcon, along with the stunning incompetence of the Death Star's gunners, saved the day. And the rest is history.