The kernel source tree does not cover the entire operating system; it only covers the kernel as a standalone unit. The tree part of it comes from the fact that few operating systems, even those that use microkernels, have a kernel whose source code could be considered organized if it was all in one directory. In fact, kernel source trees tend to be very large, especially for a portable kernel such as the NetBSD or the linux one. This is because the kernel needs to handle any eventuality in its low-level sphere of influence.
Normally, to modify one's kernel requires recompilation, which is why a kernel source tree is useful. Under Linux, that would be accomplished by a command to change the kernel configuration, such as make config or make menuconfig or make xconfig. One would then execute the command line make clean && make dep && make install && make modules && make modules_install -- provided one was using Linux. Most CDs containing an open source operating system will have the kernel source tree installable, but if for some reason you need to open up a gzipped tar file, try tar xvzf filename. Note that this will construct the directory structure starting from your current directory.