When confronted with enemies, choosing attack shifts you towards evil and choosing to bribe shifts you towards good.
Is this universally true? It seemed to me that it depends on what kind of enemies they are. I don't know the full list but I definitely noticed that attacking centaurs (for example) would shift alignment towards evil, whereas attacking undead creatures or many other types would not. I think it may have to do with whether or not the enemies are willing to accept bribes. If it's an enemy that will accept bribes, then choosing to attack instead will shift alignment towards evil, but if the enemy does not accept bribes then it doesn't matter whether or not you offer.
This was all based on observation during play, though, so I may not have it exactly right.
Last thing to note is that shifted alignments don't matter THAT much... the only real issue is that certain items have alignment restrictions. You can see which these are in the cluebook if you don't mind mild item spoilers. If you want to equip such an item but your alignment is wrong, you can intentionally shift your alignment, equip the item, then restore your alignment, and the item will stay equipped. Just don't remove it! Intentionally shifting your alignment towards evil is of course much easier... to shift towards good you have to bribe a lot which can mean doing annoying things like giving up all your gold or all your food.