Open the Messages app
Swipe down on the conversation list to reveal the search bar
Tap the search bar
Type a word, name, phone number, or phrase
Review the matching messages and conversations
Tap a result to open the conversation
To search within a specific conversation, open the chat and swipe down to reveal the search field
Enter the text you want to find in that conversation
Use the search results to jump to the matching message
If needed, use Spotlight Search by swiping down on the Home Screen and typing a message-related term