For that you need (at least) another two database tables: one with all words used in the forum (except for stop words) and the other one containing the IDs of all entries (and word frequencies/relevance) referencing the table with the words. Furthermore a mechanism to update this index is required (either performed every time an entry is added/edited/deleted or once per a certain period of time).

Looks for a lot of work for you ...

No way to implement the standard Google search script? I'm no programmer, so I have to ask that.