First of all it would be better to split the Author name into first and last. So you can search you first and/or last name.
It is not the search button that searches. To search through a table you make a query and specify criteria.
The way that a form is used is that you enter the criteria into the form
So make a query, based on the table, in the Author field in the criteria row enter
Code:
Like "*" & Forms!FormName!TextXX & "*"
with TextXX being the name of your textbox (found in properties)
Drag the query you just made (not the table) into the form.
What the search button do is it requeries (run again with new criteria) the query. So if you want to use a macro then just select refresh from the dropdown. If you want to use VBA then type in (this is after you select on-click in properties)