On Fedora, install Groovy with yum.
Then, download Grails and follow the guide: http://grails.org/doc/latest/guide/gettingStarted.html#requirements
Important: set correct Java and Grails home paths to be used by the engine.
Plain and simple guide for Postgres - https://community.jboss.org/wiki/InstallPostgreSQLOnFedora?_sscc=t
The only difference here was that initdb was called through:
sudo postgresql-setup initdb