[i-adj 〜い → 〜く] + [verb]
[na-adj] + に + [verb]
An adjective becomes an adverb – the "-ly" word that says how something is done – by changing its ending. An い-adjective swaps the final い for く; a な-adjective takes に. The adverb goes before the verb.
Drop the final い and add く: はやい早い → はやく早く, おおきい大きい → おおきく大きく, やさしい優しい → やさしく優しく.
Put に straight after the adjective, with no な: しずか静か → しずかに静かに, じょうず上手 → じょうず上手に, きれい → きれいに.
The same forms go before なる ("become") and する ("make"). These are separate grammar points.