The kernel exists to service system calls

System calls are usually invisible to applications
The standard C library masks syscalls as functions
The Linux implementation is not directly posix-compliant

The calling convention for system calls is like this:
Syscall arguments are stored in registers
This applies to archs where args are passed on the stack, too
On return, small negative value (-4095..-1) represent -errno, otherwise success
Libc wraps this to the Posix API (-1 on error, errno set accordingly)

To enter kernel space a special machine instruction is issued
x86: "int 0x80" (or the newer "sysenter", from PIII onwards)
ARM: "swi" a.k.a. "svc" (with different arguments in OABI and EABI)

System calls with many arguments use a different convention
We'll ignore such system calls here