We have regular telephone service just like the mainland, with standard U.S. style phone numbers. The area code for the island is 671. In some cases you may have issues calling toll free numbers from Guam.
Over the past few years competition has grown between the various communication companies. Formerly, residents had no choices but the "big 3" service providers. Guam Telephone Authority (GTA) for residential phone, Marianas Cablevision (MCV) for television, and Guamcell (now Docomo Pacific) for cellular service.
Over the past couple years each has delved into the markets of the other, expanded their offerings, and now consumers have choices. This has resulted in pretty heavy competition, which has improved the service and saved us all money. Each offers bundled services, and each has their own pros and cons. Generally services similar to that of the U.S. Mainland are available at reasonable prices for both residential and cellular service. GSM based phones from anywhere in the world generally can be used with a local SIM card, so bring your old phone along with you. Of course there will probably be a "reprogramming fee" involved.
Long distance service also has a few options here depending on how frequently you call and if you're calling the U.S. or another country. It's no more expensive to call the U.S. from here than it is to make any other long distance call from state to state.
A good option for saving money is using internet based messenger services like Skype, MSN, or Yahoo!. We also have Magic Jack on Guam being sold at both base exchanges and Kmart. All work well from here and you won't have any surprise phone bills.
As of late 2011, we have several cellular companies that offer a range of services comparable to those available in the mainland U.S. Rather than try to summarize them all here, it's far better to inquire after you arrive as promotions change from month to month and each company has their own pros and cons.
Do be aware that certain local companies charge ridiculous roaming fees, particularly for data roaming. Travel to foreign countries in Asia or back to the mainland U.S. can rack up some costly phone bills.