The best way to organize a school art fundraiser is to have the kids prepare some works in advance. It doesn't matter if you have older kids, younger kids, or a combination of both, just have a get-together (maybe on a Saturday afternoon) where everyone makes a few drawings or paintings that could be sold in a fundraiser. Decide how much money you will charge for each piece of art, and given how much you need to raise in total, that will tell you how many works of art you will need available to sell for your school art fundraiser.
There are a number of ways you can go about getting the art out to the public. Perhaps each child would like to be responsible for selling their own artwork, in which case they can approach family members or neighbours and explain what the school art fundraiser is about. It's a pretty easy sell, seeing as the artwork itself will show them exactly where their donation money is going, and who doesn't want to support the development of children?
You can also have an event at the school, or sell the artworks as part of another event. If you display the works, then people can browse through and maybe buy more than one. It just depends on your logistical situation how you want to set up your school art fundraiser, and you can be as creative as you want coming up with ways to get that artwork out there, and get some funds in for the school!