Generally phones are unlocked so they can be used on other networks. So if you bought a Cingular phone...you could use it on T-Mobile, for example. Here is how you can unlock a phone.

[edit] Steps

Talk to your local cellular sales representative - some companies are happy to unlock a phone if it's from one of their rivals. Also, if you say you are travelling to another country and need to use a local carrier there, they may unlock the phone for you. Many cellular providers will give you the unlock code if you had been a customer of theirs, using the phone you are trying to unlock, for a certain period of time.
Check forums dedicated to cell phone unlocking. It's a great resource with a lot of people who are very knowledgeable. Sometimes there are special tools (such as Motorola's RSS software for iDen phones) which can unlock phones from a computer. In some cases, you must e-mail a file from your phone received with said software to a hacker, which can unlock the file and send it back to you. After loading the file back onto your phone, the phone is unlocked.

[edit] Tips

Although it is always a good idea to let professionals do the work some phones can easily be unlocked. For example DCT3 and DCT4 Nokia phones can be unlocked for free, the software is widely available on the net. Free unlocking is also possible for old models of Sony Ericsson, Panasonic, Siemens and some other.
If all else fails, deliver to your local mobile phone repair shop. They can try to fix it.
If you purchased the phone through the wireless service provider like T-Mobile, Cingular etc., the Customer Service Representative can provide you detailed information and unlock codes after a few months of service. Travelling out of country on a GSM phone/network is one of the common reasons why you may need to unlock your phone. Without it, you would not be able to use the SIM card from another provider in the new country.

[edit] Warnings

Be sure to backup important information from your phone [Contacts, Messages etc].
Make copies of all files downloaded from your phone *before* they are modified. If something is wrong with the modified copy, you can reload the unmodified one to go "back to normal" in many cases.