Katie,

You can find moving boxes just about anywhere -- many office supplies companies and moving companies sell them, or you can buy them and have them shipped to you overnight from a variety of online dealers, like shop4boxes.com. There are ways to get boxes more cheaply by re-using them from groceries stories, liquore stores, etc. But beware re-used boxes, they might be flimsy and fall apart in a move.

As far as shipping, check out the large parcel centers, UPS, etc., if it's just a few boxes. There are also firms that will help you ship small loads, like minimoves.com. This article has more information on small moves.  Whoever you use, be sure to ask for references.