While every incident that causes damage to an airplane is different, especially ones where passengers, crew, or third parties are injured or killed, airlines have a general set of protocols. As Wendover Productions explains, one of the big early decisions is whether to accept or deflect blame.
One interesting aspect he mentions is how "newsy" the crash footage is, by which he means how visually interesting is the crash. A fiery crash gets way more media coverage, and that can affect how the airline responds. And commercial airline incidents almost always get more coverage because of how many people are fascinated/terrified by air travel.
Airlines' Protocol for After a Plane Crash (Wendover Productions)
Image: YouTube / Wendover Productions