Are you on Linux or windows? If you let me know I can give you detailed install and run instructions for either OS.
However, if you have already installed Nmap, use this command:
nmap -sS -P0 -O 10.1.1.1
Replace 10.1.1.1 with the server IP. This will give you a list of all the open ports, as well as the Operating System on the Server, and this is the quickest but effective way of doing it. The -P0 is a zero, not the letter 'O', whereas the -O before the 10.1.1.1 is a letter in the alphabet. This command can be run either from the server, or from a remote host.
-Stephen