ものだ

ものだ presents something as the way things are: what people are like, what naturally happens, what anyone with sense does. It goes after the plain form of a verb or an い-adjective, and after a な-adjective with な.

What you should do

The same sense of "the way things are" turns into advice: this is what a person does, so you should do it too. The negative is ものではない, "you don't do that".

べきだ gives the speaker's own judgement of what is right. ものだ appeals to common sense, as if anyone would agree, which makes it the voice of parents and teachers.

Remembering the past: 〜たものだ

After a た-form, ものだ looks back fondly on something that used to happen again and again: "I used to…".

It needs a habit from well in the past. A single recent event does not take it: ×昨日映画を見たものだ → きのう昨日えいが映画をみた見た.

Usage notes

These go beyond stating how things are.

Exclamations

ものだ can carry surprise, admiration or exasperation, often with なあ or よく.

〜たいものだ

After a 〜たい form, ものだ turns a wish into a heartfelt one.

もんだ

In speech ものだ shortens to もんだ, and ものではない to もんじゃない.