http://www.nessus.org is the tool of my choice if I want to scan my network for vulnerabilities.
Say like this, I want to know if my network is safe from dangerous people that want to mess up my network, I need to know are there any "holes" that can be an advantage to those people. So I run my tenable nessus from my PC, scan all computers in my network, and the nessus will provide me details of all vulnerabilities.
They'll also give you the details of each vulnerabilities, which ports are currently open, what's the meaning of it, is it dangerous, the links to the description, etc.
To start trying nessus is very easy, first you can download it for free from http://www.nessus.org/download/, get your activation code free for home usage, and start installing it.
This is the look of your nessus once installed, you can start by clicking on the "Start Scan Task" button to start scanning vulnerabilities.
Enter the hostname or the IP address of the computer you want to scan.
The above information will be given to show you the status of the scan.
And last you will be given the result of the scan in html format, below is the example of the report:
I highly recommend that you use nessus to scan for vulnerabilities in your network, it also gives you some info about the network, for newbies, you can learn about ports, which port is used for what.