Here's how it's used:
* "I'm feeling a bit under the weather, to coin a phrase." (This implies that "under the weather" is a well-known phrase, but the speaker is using it slightly ironically.)
* "He's a real go-getter, to coin a phrase." (This implies that "go-getter" is a common phrase, but the speaker is using it with emphasis.)
It's important to note that the idiom itself is a bit ironic. The phrase "to coin a phrase" is actually quite common, so it's technically not a newly coined phrase. But it's used to highlight the speaker's creativity or emphasize a particular point.