These steps are for a brand new install of SDL Tridion 2013 SP1 connecting to an Oracle 12c database:
First you need to make sure you have followed all the steps from the manual in regards to configuring your Oracle database server: http://docs.sdl.com/LiveContent/web/pub.xql?action=home&pub=SDL%20Tridion%20full%20documentation-v1&lang=en-US#url=/LiveContent/web/search.xql%3Fc%3Dt%26pub%3DSDL+Tridion+full+documentation-v1%26lang%3Den-US%26action%3Dsearch%26query%3Doracle&sid=lcSearch.runSearch1450779862431¤tQuery=oracle¤tScope=&eventType=lcContent.loadDocGUID-83B77343-A2E0-4114-889D-CF952BC5612C&docid=GUID-83B77343-A2E0-4114-889D-CF952BC5612C&addHistory=true&query=oracle&scope=&tid=8c86575f-aecc-4189-aa0d-96dbe2dfa8ce&filename=GUID-83B77343-A2E0-4114-889D-CF952BC5612C.xml&resource=&inner_id=&toc=false
Next you need to need to ensure you have the correct Oracle client software installed on your Content Manager. The steps are explained here: http://docs.sdl.com/LiveContent/web/pub.xql?action=home&pub=SDL%20Tridion%20full%20documentation-v1&lang=en-US#url=/LiveContent/web/search.xql%3Fc%3Dt%26pub%3DSDL+Tridion+full+documentation-v1%26lang%3Den-US%26action%3Dsearch%26query%3Doracle&sid=lcSearch.runSearch1450779862431¤tQuery=oracle¤tScope=&eventType=lcContent.loadDocGUID-19199E60-4989-4F63-82AC-92B588A46590&docid=GUID-19199E60-4989-4F63-82AC-92B588A46590&addHistory=true&query=&scope=&tid=&filename=GUID-19199E60-4989-4F63-82AC-92B588A46590.xml&resource=&inner_id=&toc=false
The ODAC Component that worked great for me was this one: http://www.oracle.com/technetwork/database/windows/downloads/index-090165.html
I downloaded the 64-bit ODAC 12c Release 4 (12.1.0.2.4) for Windows x64
You can then install the required items which are Oracle Services for Microsoft Transaction Server and Oracle Data Provider for .NET.
After installing this and, configuring your TNSNAMES.ORA file correctly and then restarting your server you should be able to run the Content Manager installer.