The author does not know what she is talking about. mmap is a system call in Linux.
Back to your question, open a terminal and type man mmap or read this:
http://man7.org/linux/man-pages/man2/mmap.2.html
To use mmap, the simplest way is to use the library function mmap(). You can call the function from your assembly code.
Here be dragons.
If you want to deal with system call, you can use the syscall() function in libc. You will need to figure out the actual mmap syscall to use. There are two mmap syscalls: mmap and mmap2 due to evolution of the Linux kernel ABI to handle big files on 32-bit systems. And the arguments for mmap syscalls may not be the same as the libc wrapper function. Luckily for x86_64, there is only one mmap syscall and it takes the same arguments as the libc API. You you can do something in C like:
fd = open(...);
fstat(fd, &buf);
result = syscall(__NR_mmap, NULL, buf.st_size, PROT_READ, MAP_PRIVATE, fd, 0);
If you really want to deal the x86 syscall instruction, it is quite easy to convert the call to syscall() above to direct use of the syscall instruction.
Have fun hacking.