* "Mettre" is the most common and versatile verb for "put" in French. It can be used in many contexts, such as "put on a coat" (mettre un manteau), "put a book on the table" (mettre un livre sur la table), or "put the phone down" (mettre le téléphone).
* "Poser" is used specifically for placing something on a surface, often gently. For example, "put the glass on the table" (poser le verre sur la table).
* "Placer" is used for placing something in a specific location or position, often with care. For example, "put the flowers in the vase" (placer les fleurs dans le vase).
The best way to choose the right word is to consider the context and the action being performed.