When she saw the dress, she just couldn't help laughing.

Literal

She [topic-は] that dress [object-を] saw when no-matter-what laugh-without could-not-be.

~ずにはいられない is the canonical 'can't help but' construction — combining the classical negative ~ず ('without'), the topic-marking は (here for emphasis), and いられない (negative potential of いる 'be / exist'). Literally 'can't be without doing X'. どうにも ('no matter what one tries, in any way') intensifies the helplessness: 'I just couldn't, no matter what'. The whole sentence is a textbook setup for showing how Japanese builds expressive emphasis by stacking grammatical pieces — classical ず, は, potential いる — into something with real rhythmic force.