These are some of the more important system calls to use when dealing with Linux. For most cases, however, it is best to use library functions rather than direct system calls, because the system calls were designed to be minimalistic while the library functions were designed to be easy to program with. For information about the Linux C library, see the manual at http://www.gnu.org/software/libc/manual/
Remember that %eax holds the system call numbers, and that the return values and error codes are also stored in %eax.
A more complete listing of system calls, along with additional information is available at http://www.lxhp.in-berlin.de/lhpsyscal.html You can also get more information about a system call by typing in man 2 SYSCALLNAME which will return you the information about the system call from section 2 of the UNIX manual. However, this refers to the usage of the system call from the C programming language, and may or may not be directly helpful.
For information on how system calls are implemented on Linux, see the Linux Kernel 2.4 Internals section on how system calls are implemented at http://www.faqs.org/docs/kernel_2_4/lki-2.html#ss2.11