There is no specific set of rites or ritual you need to perform to ascend to Daemon Prince. The process is very unclear.
Each current Daemon Prince had to commit countless atrocities to even gain the attention of it's chosen Chaos god. There's usually some subconcious urge to complete a task or slay a specific foe, once this is accomplished, you would know that the reward is ascension.
The closest thing to an actual guide would be somthing like:
- Kill a lot of people
- Kill even more people
- Let everyone know you really like Khorne
- Kill even more people while letting them know you really like Khorne
- Start hearing Khornes voice in your head
- Receive blessings from Khorne, power, gifts(mutations / ability to shoot fireballs and such), weapons, armour, etc.
- Kill many thousands more people
- Live for centuries, all the while killing and talking about how great Khorne is
- Realize what it is you need to do to ascend... (kill this guy or blow up this planet)
- Do that thing
- Bingo! Now you have wings.
It's never specifically addressed in the fluff and I think this is very deliberate. Each Chaos Champion has to do somthing different if they wish to ascend, this leaves the Games Workshop and it's writers freedom to create different and unique stories for each prince.
Primarchs get special treatment, they just need to ask and a Chaos god will snap them up.