〜出す
suddenly start doing, burst into
Verb ます-stem + 出す
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Add 出す to the ます-stem and the action bursts out, suddenly and often without warning: 急に雨が降り出した, "it suddenly started pouring". Compare 降り始めた, which just says it started.
It's common with things that happen to people, or with the weather, rather than planned actions: 泣き出す, "burst into tears"; 笑い出す, "burst out laughing"; 走り出す, "break into a run".
Because it suggests something unplanned, it's odd with deliberate starts. For "I started studying Japanese last year", use 始める, not 出す.
It conjugates like 出す itself, a godan verb: 出した, 出して, 出しそう.
Examples
急に雨が降り出した。
It suddenly started raining.
赤ちゃんが急に泣き出しました。
The baby suddenly burst into tears.
みんなが一斉に笑い出した。
Everyone burst out laughing at once.
信号が青になると、車が走り出しました。
When the light turned green, the cars pulled away.
その話を聞いて、彼は急に怒り出した。
When he heard that, he suddenly got angry.