This is how it works. There will be a repository(Management Server) where the information(nodes,databases and preffered credentials for those databases etc) will be stored. And on each database there will be an intelligent agent(DBSNMP) and data gatherer. When you schedule any job,task all the preliminary checks will be performaed in the management server and then the task will be submitted to intelligent agent which performs the task and reports back the results back to managemnt server.

either you can specify management server, if you have installed repository. Otherwise directly you can use couple of components of OEM like DBAstudio etc directly connecting database you have on the box.

Just pick up dbastudio and say connect to local database, give userid and password. It will ask you to create connection string and updates OEM tnsnames.ora.

Hope this helps. REad Documentation for the rest.