Depending on how users use them, machine-translation programs can produce significantly better results.

Literal

English-Japanese translation software [topic-は] user [genitive-の] usage [depending on-次第で] translation results [object-を] significantly can-improve.

A software/tech sentence. ~次第で ('depending on X,' 'determined by X') is a formal dependency marker, similar to ~によって but emphasizing that the outcome varies with the value of X. Common collocations: 天気次第で (depending on the weather), 君次第だ ('it's up to you'). 使い方 ('way of using,' 'how to use') is noun form from the pattern [verb stem]方 ('way of X-ing'), same as 書き方, 読み方, 作り方. 大きく改善できます combines a manner adverb (大きく from 大きい 'big') with the potential of 改善する ('improve'): 'can greatly improve.'