First, preexisting rocks must weather/erode, forming the sediment that will eventually form the sedimentary rock. Then, that sediment must settle someplace, and over a long period of time, pressure begins to build. This causes the sediments to become compacted. After a long period of time (and a lot of pressure), the sediments cement together and form a sedimentary rock. In a nutshell, sedimentary rocks form through compaction, cementation, and eventually... lithification.
Hope that helped!