Simple:
* She patiently waited for the bus.
* He patiently explained the instructions.
With context:
* The teacher patiently answered all of the students' questions.
* The doctor patiently listened to the patient's concerns.
* Despite the long line, she patiently waited her turn.
* He patiently worked through the complex problem.
Figurative:
* The old tree patiently watched the seasons change.
* The sculptor patiently shaped the clay into a masterpiece.
As an adverb:
* The artist worked patiently for hours on her painting.
* She spoke patiently to the upset customer.
As part of a phrase:
* He waited patiently and quietly for the news.
* She responded with patience and understanding.