open isn't a shell command or a program name, it is a system call. Ultimately all normal programs are implemented using these operations, but in the case of shell script this is hidden from the user (as it is very fiddly). The shell provides a simpler interface for doing file operations than open and friends.
When you read a manual page, check the section number (in brackets after the page name at the top left). Section 1 documents commands and programs which can be used from the shell, section 2 documents system calls (like open). Section 3 documents library calls (again, these can be used from C programs). See the man manual page for a list of what all the sections contain.
For example, if you want to read the contents of a file line by line, you don't explicitly open it, you use standard input re-direction, like this:
while read line; do echo "I read this: $line"; done < input_file
Which will read lines from the file "input_file" and print each one, prefixing each line with "I read this: ".
To get an idea of how to program in the shell, I recommend having a read a shell tutorial. Don't be discouraged - it can seem a little intimidating at first, but if you can spend some effort to learn it, you will be able to do all sorts of cool stuff with ease which is a massive pain to do in other ways.
Have a look here: http://tldp.org/HOWTO/Bash-Prog-Intro-HOWTO.html
This re-direction thing I mentioned above will hopefully be a lot clearer after you've read that part of the guide. Learn what it means: stdout, stdin, stderr, redirection.