第【dì】

第 before a number makes it an ordinal: 第一 "first", 第二 "second", 第十 "tenth". As with any number, a measure word goes between it and a noun.

• × 第三人 → 第三个人

二, not 两

After 第 the number is always 二, never 两. 两 counts; 第二 is a position.

• × 第两天 → 第二天

In a story, 第二天 is "the next day".

第几: which one?

第几 asks for a position.

Numbers without 第

Dates, floors, school years and numbered rooms or buses take a bare number: 五月 "May", 三楼 "the third floor", 二年级 "second year", 八路车 "the number 8 bus".

Watch the month: 一月 is "January", but 一个月 is "one month".