Sandstone, siltstone, shale.The three rocks above are all made up of very, very small sediments. What is the name of the process which takes these...

It is called diagenesis. Diagenesis occurs in several stages. First, compaction happens as the particles are pressed together by the increasing weight of what is above. The size of the spaces between is reduced, and water is forced out. As new minerals fill in the remaining space, cementation occurs, and particles bind together. Further steps can occur later, if compression continues and the rock hardens further. The below link is a good source for more info.