String searching in standard SQL uses the LIKE operator, which Sequel supports using the like method and a string.
MySQL and PostgreSQL both support string searching using regular expressions, though they use different syntax. Sequel allows the same ruby code to work on both databases, using a ruby regular expression as the argument to the like method.
Microsoft SQL Server, MySQL, and PostgreSQL all support full text searching, all using different syntax. The Sequel code to support them is the same in all cases, giving the columns and search terms as arguments to the full_text_search dataset method.