Its just like any other organization that fundraises...
Usually the benefiting committee will do the leg work. For example, if the youth want to take a trip they will determine what the fundraiser will be and all of the details.
If its something for the church...like the "building fund"..the church leadership (ie-deacons) will determine it and appoint someone to chair the fundraising committee.
Most churches however don't call everything thats a fundraiser, a "fundraiser". There are certain events that happen during the year that they expect to make a certain amount of money off of to include in the operating budget. So the annual Christmas play or annual anniversary concert where tickets are sold....is a fundraiser in a "kind-a-sorta" way. <<<<and this goes for any type of organization.