Generally a serchbox is just a textinput. The gallery is where the code goes that makes the magic happen. In your gallery.Items property you would filter the results based on what was typed in the search box. The real issue is the fact that you will more than likely like the the searchbox the best when you use the In function but that function is non-delegable. Here is with and without the In function:
Equals a value (fully delegable but search has to match exact string)
Filter(SPListName, ColumnName = SearchBar.Text)
Found in a value (not delegable but will find any matching substring in the column value)
Filter(SPListName, SearchBar.Text In ColumnName)
Starts with a value
Filter(SPListName, StartsWith(ColumnName, SearchBar.Text)
You could also look into search as well... many options depending on your situation and number of entries in list etc. Basically the idea is to filter the gallery on the user's input into the 'search box' control.