Depends slightly on whether you mean a committee of young people or a committee that runs the youth club? If its the latter then they would have legal responsibility for all aspects of operating the club - generally you'd need a constitution, a few policies in place (child protection, health & safety, confidentiality, equal opps etc.), to make sure staff & volunteers are suitable, effective and supported, to ensure activities are safe & appropriate (including risk assessments), and to link to the former to ensure that young people attending are able to participate in the running of things.
Getting young people involved in committees isn't simple - it takes time & planning. You can just throw some onto a committee and this can work in the short tem but generally you'll find you get back from them what you invest. In terms of how to invest think about what opportunities there are for young people to contribute, what sorts of young people are involved with the club and what skills they have and how you can use them and then look for gaps and how you can help address these - for instance if the young people involved don't listen too well then you can look to work on that, or if they lack in clear leadership you might want to look at how you can create opportunities for them to develop skills & and an understanding of leadership & cooperation.
Obviously its much more involved than this but hopefully that will help to get you started! Also you can download some model policies & information sheets (for free) from our website - go to www.yomo.co.uk/remository/ and have a look through some of the sheets (all in pdf format).
We also have some things that can help with young people getting involved in committees - Dilemmas is a card based activity that helps participants understand the process of having an effective meeting - and DISCussion is a an alternative method for running a meeting - designed to allow everyone to contribute to the 'minutes' and to rotate the role of chairperson - you can find these on the yomo.co.uk site too in the 'Resources' section.
Good luck!