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You'd add it just like a regular Java class:
Logger log = Logger.getLogger(getClass()) // log4j
or
Log log = LogFactory.getLog(getClass()) // commons logging
Using the standard Log4j's new Logger(getClass()) worked, but logged 'java.lang.Class' for me (using Grails 1.2.1). This problem went away with the Sublog plugin and @WithLog. See http://www.grails.org/plugin/sublog. This plugin also does not make Trace become Debug and Fatal Error...!