TCP (Transmission Control Protocol) and UDP (User Datagram Protocol) are two of the protocols that make up the TCP/IP protocol suite which is used universally to communicate on the Internet. Each of these has ports 0 through 65535 available so essentially there are more than 65,000 doors to lock.
The first 1024 TCP ports are called the Well-Known Ports and are associated with standard services such as FTP, HTTP, SMTP or DNS. Some of the addresses over 1023 also have commonly associated services, but the majority of these ports are not associated with any service and are available for a program or application to use to communicate on.
Port scanning software, in its most basic state, simply sends out a request to connect to the target computer on each port sequentially and makes a note of which ports responded or seem open to more in-depth probing.
If the port scan is being done with malicious intent, the intruder would generally prefer to go undetected. Network security applications can be configured to alert administrators if they detect connection requests across a broad range of ports from a single host. To get around this the intruder can do the port scan in strobe or stealth mode. Strobing limits the ports to a smaller target set rather than blanket scanning all 65536 ports. Stealth scanning uses techniques such as slowing the scan. By scanning the ports over a much longer period of time you reduce the chance that the target will trigger an alert.
By setting different TCP flags or sending different types of TCP packets the port scan can generate different results or locate open ports in different ways. A SYN scan will tell the port scanner which ports are listening and which are not depending on the type of response generated. A FIN scan will generate a response from closed ports- but ports that are open and listening will not send a response, so the port scanner will be able to determine which ports are open and which are not.
There are a number of different methods to perform the actual port scans as well as tricks to hide the true source of port scan. You can read more about some of these by visiting these web sites: Port Scanning or Network Probes Explained.
It is possible to monitor your network for port scans. The trick, as with most things in information security, is to find the right balance between network performance and network safety. You could monitor for SYN scans by logging any attempt to send a SYN packet to a port that isn't open or listening. However, rather than being alerted every time a single attempt occurs- and possibly being awakened in the middle of the night for an otherwise innocent mistake- you should decide on thresholds to trigger the alert. For instance you might say that if there are more than 10 SYN packet attempts to non-listening ports in a given minute that an alert should be triggered. You could design filters and traps to detect a variety of port scan methods- watching for a spike in FIN packets or just an anomylous number of connection attempts to a variety of ports and / or IP addresses from a single IP source.
To help ensure that your network is protected and secure you may wish to perform your own port scans. A MAJOR caveat here is to ensure you have the approval of all the powers that be before embarking on this project lest you find yourself on the wrong side of the law. To get accurate results it may be best to perform the port scan from a remote location using non-company equipment and a different ISP. Using software such as NMap you can scan a range of IP addresses and ports and find out what an attacker would see if they were to port scan your network. NMap in particular allows you to control almost every aspect of the scan and perform various types of port scans to fit your needs.
Once you find out what ports respond as being open by port scanning your own network you can begin to work on determining whether its actually necessary for those ports to be accessible from outside your network. If they're not necessary you should shut them down or block them. If they are necessary, you can begin to research what sorts of vulnerabilities and exploits your network is open to by having these ports accessible and work to apply the appropriate patches or mitigation to protect your network as much as possible.