This crafting system has two machines, the Maker and the Stamper. These machines need to be used with a tube system to make them really automatic. There's also a machine called the Packager, simply it tries to craft anything you give it into 2x2 or 3x3 blocks for storage.
The Maker makes craftpackets. This is fueled by paper, which goes in the bottom slot. Then you need to select which crafting slots items will go in. Place items in the top slot to put those items into a craftpacket. When there are items in all the selected slots, the craftpacket will be moved to the right slot. If the craftpacket is blue, that means it can be crafted into something.
Place craftpackets in the left slot of stamper to craft the packet. If you place an invalid or incomplete craftpacket in, the contents will be dumped to the other slot. You can also put in, for example, bones to get bonemeal. If a recipe has multiple results, such as for making cake, all the other used ingredients will be placed into the output slot.
There is another crafting machine, the Packager, which will try crafting a 3x3 or 2x2 grid full of whatever item you give it. This is quite useful for automatically making bricks and if you have GregTech disabled, metal storage blocks.