Use it when you've got explicit permission, not just because there's no rule against it. I'm at liberty to use the car since Mom said I could.
Pro Tip 2/3
Not Obliged
It suggests a choice, meaning you're not obliged or expected to do something. You're at liberty to leave the event early if you want.
Pro Tip 3/3
Formal Context
It's more formal and may sound outdated in casual conversations. Use it in writing or formal speech. You are at liberty to submit your complaint in writing.