How to apply for passport after registering child as british

I applied to register my UK born child as a british citizen after my ILR and have received the certificate now.. Can somebody please let me know the process for applying for passport.

Is there a fast service? how much time does it take and also what documents do i need to send?

Thanks in advance.

Have you read the Passport FAQ?

See Citizenship FAQs - Common Questions - Read before posting - Passport.