This is something people get confused on a lot.
What sort of multiple word searching are you after? AND (all words required), OR (any word required), or some sort of qualitative matching scheme with confidence values?
For the first two, you can get around the problem to a degree by dynamically building your SQL query depending on how many keyowrds were specified by the user. Example pseudocode below:
$query = "SELECT blah FROM blahtable WHERE";
$query .= "related LIKE '%$word%'";
loop through keywords
$query .= " AND related LIKE '%$key%'";
end loop
very unclear code I know but you get the picture. It shows an AND match - just substitute the AND for OR to get 'any word' style matching.
Qualitative matching is a different kettle of fish altogether - you'd probably need to write an extension to your database server for that...