Observing with

観(み)る means to watch or observe something attentively, especially a performance, film, or event. The more common spelling 見(み)る covers a broader range of seeing and watching.

Examples

Shall we go see a movie with 観る

Manga panel from アオハライド showing example of Shall we go see a movie with 観る.
アオハライド » Volume 12 » Page 42

After talking with her boyfriend in the hall, Futaba returns to her classroom and walks over to her friends.

双葉(ふたば):
「この映画(えいが)一緒(いっしょ)に観(み)に行(い)かない?」
“How about going to see this movie?”
悠里(ゆうり):
「え どの映画(えいが)?」
“Oh, which movie?”

Watching the news with 観る

Manga panel from からかい上手の(元)高木さん showing example of Watching the news with 観る.
からかい上手の(元)高木さん » Volume 1 » Page 113

As Nishikata watches the news, his daughter sits down to watch.

西片(にしかた):
「ちーはニュースも観(み)るのかー。」
“You watch the news too, huh, Chi?”
ちー:
「テレビすきー。」
“I like television.”

Supplemental Examples