第一 + [noun] [noun] + が第一だ [noun] + を第一に + [verb] [noun] + 第一 第一、[sentence] 第一に、[sentence]
第一 means "first" or "number one". After a noun, with が and だ, it says that thing comes before everything else; in front of a noun it makes "the first …".
With を, the thing you put first becomes the object of a verb, usually かんがえる考える. A bare noun followed by 第一 is the slogan form you see on signs, and it takes で to describe how you act.
Set off by a comma at the head of a sentence, 第一 means "to begin with": the most basic reason something won't work. It nearly always backs up an objection or a complaint, and it belongs to speech.
With に, 第一 starts a list of points, and だいに第二に and だいさん第三に can follow. It carries no complaint and suits presentations and writing.