Europe has adopted GSM (Global System for Mobile Communications) as its mobile communications standard—unlike the US, which left companies to each create their own standards, resulting in largely incompatible networks. Settling on the GSM standard makes it easy to buy a cell phone that works in every European and Asian country, but there are some things you need to know.
What You'll Need in a GSM Cellular Phone and SIM card
To make cell phone calls in Europe you'll need an unlocked dual-band GSM phone and a SIM card.
The countries of Europe use the dual band frequencies of 900-1800. The US uses mainly 850-1900. You'll want a tri-band 900/1800/1900 (or 850/1800/1900) or, better yet, a quad-band 850-900-1800-1900 if you intend to use the phone in the US as well as in Europe. You may use a tri-band 850-1800-1900 unlocked cell phone in Europe, but you'll be giving up coverage in the 900 band, which is the most common band for international cell phone communications.
Many companies in the US sell locked cell phones which provide only one SIM card option for use with each phone linked to one particular carrier. This is called a "locked" phone. This is not what you want. Unlocked cell phones allow the use of any SIM card, as long as the frequency capabilities are correct. Unlocked GSM phones are what you need.
You can check your US carrier to see what roaming costs, but with the low cost of cell phones and international SIM cards, you might be better off just buying an unlocked cell phone like the LG Optimus L5, which sells for less than $100.
Note the "World" in its description; this is a way you can assure yourself that it will work overseas. That said, my Nexus phone works just fine with an Italian SIM.
You can also request that your carrier unlock your current locked phone.
The postage stamp sized SIM (Subscriber Identity Module) card is the heart and brains of the cell phone.
The SIM card will determine the phone's number and allow access to the services that particular SIM card supports. Folks generally buy a SIM for (not in!) the country they expect to make calls from. Prices vary with country and services. With a prepaid card, you'll probably receive unlimited incoming calls from anywhere in the world, some free calling time and fairly reasonable long-distance rates (around half a Euro per minute to the US). There is often a service life of the card that you can extend by purchasing airtime vouchers in the country you're visiting--usually at convenience markets, gas stations, and news kiosks. A postpaid SIM card requires a contract that usually bills monthly.
Where do I get my Unlocked Cell Phone and SIM card?
Not long ago you were best off purchasing your cell phone and SIM card in the US from a dealer who specializes in selling and renting cell phones for use abroad (This is especially true for the SIM card itself since until recently most countries in Europe sold SIM cards only to residents). One benefit of getting the card early is that the number of your phone is embedded in the card, so you'll be able to give that number out to family and friends.
You'll activate the SIM when you get to your destination. You can easily add calling time to the original SIM so you don't have to change numbers each time you run out of call time.
These days it's not hard to just go to a country and buy a SIM card at a very reasonable price. The Italian cards we buy where we're in Italy are good for a year, have free incoming calls and messages, and you can buy minutes as you go and refill from any of the many outlets, including newsstands, that recharge phones (or you can recharge your SIM online).
You can also rent a GSM cell phone. Some come with auto rentals and leases. But the rent on the phone along with the high usage rate often makes purchase a better deal—you'll probably pay for the phone after the first trip if you make many calls.