After the having applied and being contacted by CERN you'll have a Skype interview with your future supervisor and that's pretty much it. If you click then you're in. I'm not even sure that he's allowed to say no to be honest. The whole thing is not very formal. No tests of any kind apart from a conversation you have with the supervisor.

The interview process for fellows is very lightweight. Usually you will only have a phone interview and in some cases a personal interview. The only difficult part is to get the necessary information together for the online application (including references).