* Smiles are actions, not states: Adverbs typically modify verbs, adjectives, or other adverbs. While "smile" is a verb, it's more of an action than a state of being.
* We describe smiles, not how someone smiles: We often describe the *type* of smile (e.g., "a warm smile," "a mischievous smile") rather than how the person is smiling.
However, you can use adverbs to describe the manner of smiling:
* Warmly: "She smiled warmly at the child."
* Shyly: "He smiled shyly at the girl."
* Broadly: "He grinned broadly at the joke."
* Delightedly: "She smiled delightedly at the surprise."
* Sadly: "She smiled sadly as she recalled their memories."
You can also use phrases to modify "smile":
* With a smile: "He greeted her with a smile."
* A smile on her face: "He saw a smile on her face."
The best choice depends on the context and what you want to emphasize.