While SMF naturally incorporates a powerful search engine, knowing how to use it is not surprisingly the key to returning successful results!
Starting a Search
Assuming the forum is running the SMF default theme (or a derivative of it), there should be both a simple Search field (partnered by an Advanced search text link) in the collapsible top section and a Search option in the main menu. If not, the main menu Search option should still lead straight to the advanced search screen.
While you can just type (and search for) any combination of characters, you should consider using quotes to make your search really work for you:
To put this in a nutshell, searching for simple machines forum will return any or all of these three words, but enclosing the search string in double quote marks (ie "simple machines forum") will return only the entire phrase.
Simple or Advanced?
To use the simple search (if enabled), the basic syntax outlined above is all you really need to know. But you might also like to know that this tool searches the entire forum for any or all of what you specify that's been posted during the last 9999 days (which is more than 27 years)! So, to take more control of your search, you should use the advanced search feature.
Although the advanced search screen might initially seem a little intimidating if a forum has many boards and child boards, it's surprisingly straightforward when reduced to its basic components: