They have application deadlines in waves - check the website for the next one, sooner is better though.
You can choose to apply for multiple roles, and if you get assessed, they choose which job would best suit you, even if you didn't originally apply for it, so you might as well apply for all the roles you wouldn't mind doing. Voluntary experience seems to go down very well with them, so milk that as much as you can.
The assessment day has 30-40 applicants at it, split into groups of 10-12. You get assessed by different assessors, doing different tasks. Some tasks are group work: planning a social action project and presenting it, role-playing challenging situations you might encounter, other stuff probably. Individual work includes telling your group about a charity visit they'll be doing but keeping them interested, running an activity whilst people misbehave, presenting a pre-planned icebreaker activity, and things I can't remember.
There are also group discussions where a question is asked and people take turns answering. The questions are about why you want to work with NCS, situations you might encounter, how young people benefit, stuff like that.
Or it might be totally different outside of Manchester for all I know!