A powerful search text box would need a where clause for each search term and allow for operators. This approach you would need search terms parser to tokenize the search terms into a parse tree that you could iterate through building the search SQL where clauses.
i.e.
Brown + fox == where column like '%Brown%' and column like '%fox%'
Brown fox == where column like '%Brown%' or column like '%fox%'
"Brown fox" == where column like '%Brown fox%'
Another less powerful approach that would cover your scenario would be to replace all the spaces in your search term text box with a %.
example code in search button click event
Code:
// resulting search terms would like this: %Brown%fox%jumped%over%the%couch%
// for a text box containing: Brown fox jumped over the couch
Search(String.Format("%{0}%",txtbxSearchTerms.Text.Replace(' ', '%')));