Rivals must be selected on the RaceNet websiteNote for players of other Codemasters games on more than one platform, you will need to select the correct platform (PlayStation in this case) as your LEAD account before you can search for friends on that platform by going to his page - RaceNet Account Linking
Firstly you are given 2 rivals randomly, you could try and beat these BUT its advisable to instead boost this with a friend.
To add a Rival you will need to visit this webpage - RaceNet Rivals Page
From here add a new 'Social' Rival. Note they must first be on your PSN Friends List in order to show up in the list.
Once your Rival has been set you simply need to finish higher than they do in an event, any will do.
You can Create a gaming session for this game here