Your LA website will have the stats showing school allocations for the current year6 though PSB. This should give you an indication of how likely you are to get your preferred school.
My DS got a letter from school during September to say online applications were open and the closing date is always 31/10. Online applications are preferred - our LA does allow paper applications but I have no idea how you get one. The senior schools will all have open days/evening for you to go and have a look around too.
National Offer Day is always 1st March too.
We ended up going indy for DS as a combination of a high birth rate, moving house and an unfavourable allocation system (but totally fair and those were the risks we took) left us with a state option that we couldn't use.