there is no hard and fast rule about how to apply for one, generally if you have uploaded few videos and some of them have got popular and youtube team recognizes that those videos are your self creation than you will be sent an invitation via email.
you have to remember that the content you upload should be yours own and not copyright of someone else.
here is the email you will get
Your video might be eligible for the YouTube Partnership Programme, which allows you to make money from playbacks of your video.
Making money from your video is easy. Here's how it works: First sign in to your YouTube account. Then, review and complete the steps outlined here:
If your video is approved, we'll start placing ads next to the video and paying you a share of the revenue, as long as you meet the programme requirements.
We look forward to adding your video to the YouTube Partnership Programme.
Thanks and good luck!
The YouTube Team
