Roaming is the simplest way of using your phone abroad. You can generally use the same phone you currently have while away from home. You also keep your same phone number but it is generally much more expansive than than other methods if used for more than a couple minutes.
No new cellphone needed most of the time.
No need to buy a new SIM card.
Same phone number as back home.
No need to open cellphone to change SIM card.
Expansive, you pay extra for receiving and making calls.
Local callers in the country you're visiting will have to pay long distance to call.
Might have to call your cell phone carrier to activate roaming.
A cellphone running on the same system as the country you are visiting is required. Most countries use a GSM phone system on one of the following frequencies: 850/900/1800/1900Mhz. Many phones are quad band and run in all countries, others at tri band which will run in almost any country but possibly with a smaller coverage, and single band phones which only work on one frequency. You will have to make sure your phone works on the same frequency as the country you are visiting. You don't have to worry about this if your phone in quad band. You will know if your phone works in the country by simply turning it on when arriving and seeing if it displays the name or logo of a service provider.
The phone can be unlocked or locked.
You might need to call your cell phone provider to activate roaming on your phone. To do so simply call the customer service phone number of your cellular provider and ask them to activate roaming.
Using roaming while in a foreign country can be expansive. The prices range depending on your cellular provider and the country you are visiting. You can expect a range of 2-5 dollars/min while call or receiving while abroad. Calling a local number is generally less expansive than calling a number back home. Calling a number in a different country (other than the one you are currently visiting and your home) will generally be more expansive and might require activation from your provider.
When someone calls your number from home, they will pay as a local call and not be charges extra, however you will still have to pay if you answer. When a local person calls your phone, they will be paying as a long distance number and you will also be paying to receive the call.
To summarize, this is a good option if you plan on using your cellphone for less than 10 minutes while abroad or going for a very short time. It is expensive but does not require any new cellphone and you keep your same home number.
For additional information you can visit the wikipedia article about roaming. It is located at: http://en.wikipedia.org/wiki/Roaming.