Hi Mr_Mister,
I hope you have configured Activiti and Activiti Explorer is up and running. If thats the case, go to the webapps\activiti-explorer\WEB-INF\classes\db.properties under your tomcat installation (inside your activiti home directory) change the connection paramters to use your mysql. If you want to change the way in activiti-rest interface work, go to webapps\activiti-rest\WEB-INF\classes and edit activiti.cfg.xml. Restart tomcat and your activiti tools should be now pointing to your database. Hope this helps.
Thanks,
MuraliRam