If for whatever reason you need to search an entire database (and you don't have PhpMyAdmin available to you) then a really quick and easy way is to use mysqldump and grep.
First do a mysqldump of the database you want to search:
mysqldump -uUSERNAME -p DATABASE_NAME > database-dump.sql
Replacing USERNAME and DATABASE_NAME with your respective details, for more on mysqldump go here: LINK
Once you've got your database in a file just grep!
grep -i database-dump.sql "Search string"
Easy huh :)