Patching the kernel of a running system is the most efficient method of rootkitting (i.e. hiding the attacker's presence on the system and any use made of systems resources for illicit purposes, which includes files, processes and network connections).
See also past lecture notes for references to kernel system call hijacking, especially Phrack 58:6 Phrack 59:5 [local Phrack mirror].
I suggest the cross-referenced Linux code project http://lxr.linux.no for looking at kernel code. Most likely, you will want to start with a particular function or variable, i.e. a "symbol" in linking terms, so you will start with "Identifier search". "Freetext search" is useful when you don't know the exact symbol name. Symbol names in LXR are links to the place where the symbol is defined. Sometimes the definition is detected incorrectly (kernel macros are quite complex, and LXR only does regexp matching), then "Freetext search" also helps.
There is no single "good starting point" for looking at kernel code, but Phrack articles name the most sensitive pieces security-wise, and http://kernelnewbies.org/ will help.