Grammar JLPT Level N4 - Lesson 1

Structure of 段々(だんだん):

だんだん + （と） + Phrase

Details about 段々(だんだん):

だんだん is an adverb that is used to express the slight, but constant, progression of something. Originally, it comes from the kanji construction 段々(だんだん), which can be thought of as meaning 'step by step', 'stepwise', or even 'steadily'. だんだん is similar to ほとんど, in that it can modify the meaning of entire phrases, rather than just single words.
To use だんだん, simply put it before the phrase that you want to express as '(A) that is increasing steadily'.

12月(がつ)になってからだんだん寒(さむ)くなってきた。
Since December, it has gotten colder steadily.
だんだん仕事(しごと)の環境(かんきょう)に慣(な)れてきた。
I have steadily gotten used to work's environment.

While だんだん can take the particle と, it is not required. In fact, と is very often omitted from adverbs/onomatopoeic words (words that represent a sound or motion) in Japanese.

最近(さいきん)はだんだんと暑(あつ)くなってきたね。
Recently it has progressively gotten hotter, right? (Slow progression)

段々(だんだん)

Usage Notes for 段々(だんだん):

Initially, it can be easy to mix-up だんだん, with どんどん. どんどん is an onomatopoeic word that represents loud banging (like on a drum), so is used to express fast changes/progression. This is unlike だんだん, which expresses slower changes/progression.

だんだん雨(あめ)が降(ふ)ってきた。
It is starting to rain. (Slow progression, does not imply great speed or severity)
どんどん雨(あめ)が降(ふ)ってきた。
It is starting to rain. (Rapid progression, may imply great speed and/or severity)