Hackers, by nature are very stealthy. Their ability to gain access to your computer through the Internet can easily be done without your knowledge - and most of them seem to prefer that approach. Before time is spent on being able to detect a hacker, it should be noted that a determined hacker will not be stopped! They will get in - even to the Department of Defenses systems!
Some common things that might tip you off to an intrusion are:
Lights showing hard drive activity being busier than what your own activities call for
Suspicious files left on your computer - often in the Windows Temp directory with a tmp. suffix
Obvious tampering - destroyed files, missing files, etc.
Or, the worst case - someone's taking money out of your bank account or using your credit cards (Please note, though, that this could also be the result of phishing, too - not necessarily hacking)
Your firewall keeps receives multiple packets from a single web address and notifies you.
Once a hacker does gain access to your computer, he will purposefully leave a little file or two, that will give him easy access in the future. These files are usually referred to as "trojans." This is one of the facts about hackers that is not very comforting.
One free program that you might use in order to learn of the hacker's IP address is Netstat. This Windows program will enable you to see exactly what the hacker does - tracing everything. It also shows you the status of all of your ports, and other statistics.
Besides needing an IP address, you must also learn the ISP from which the attack comes. Port 43 will give you data about the IP and the ISP. Software is available that can tell you these things, and you can also learn about it by going to a whois directory. Then, with this information, you can contact the Webmaster of the ISP, and hopefully, get it stopped.
Each of us needs to take some serious precautions about preventing our own computers from being broken into (as much as possible). With the software and firewalls that are currently available, perhaps you will never need to be one who cries out, "I need a specialist, to catch a hacker". After you get the necessary programs to make your computer safer, be sure to keep it updated, and prevent computer crimes hacking.