だす, or
出（だ）す in its kanji form is a verb that is regularly attached to the
conjunctive form of other verbs. When it is connected in this way, it has the meaning of 'to suddenly do (A)', or 'to burst into (A)'.
To use this construction, simply add
だす to the ます stem (conjunctive form) of the verb that you want to highlight as happening 'suddenly'.
最初（さいしょ）から速（はや）く走（はし）りだすのは体（からだ）に良（よ）くない。
It is not good for your body if you suddenly start running fast.
転（ころ）んだ息子（むすこ）が泣（な）きだす前（まえ）に、あめをあげる。
After falling, I give my son candy before he bursts into tears.
Unlike
はじめる, another common structure which means 'to begin',
だす quite often has the nuance of being unintentional, or something that the subject cannot avoid doing (or cannot be controlled). On the other hand,
はじめる expresses the direct intention of the subject to do (A).
コンサートで歌手（かしゅ）が歌（うた）を歌（うた）い始（はじ）める。
At the concert, the singer will start singing. (Something that has been planned to be started)
最近（さいきん）、友達（ともだち）が授業（じゅぎょう）中（ちゅう）に歌（うた）いだした。
Recently, my friend suddenly burst into song during class. (Something that happened without any prior plan/expectation)