It consists (mainly) of 9 islands:
With major emigration from the Azores in the early and mid 20th century, many Azoreans have settled in Europe and Brazil, Canada and the US as well as other places around the world. It is not fair to name any one location as the tenth island (although Americans like to claim that the New England areas of New Bedford, Fall River, Provincetown, MA and Providence, R.I. are the 10th island). In any case, the Azorean Diaspora is strong and proud of their history and ancestry. To solve the problem dispersing away from the islands has caused, the Global Village of Azores Nation  has sprung up to help unite the Diaspora in the true tenth island, online where thousands of people from and connected to the Azores gather to socialize and share stories from their lives, wherever they may live now.
These nine volcanic islands are situated in the northern Atlantic, about 1,500 km (950 mi) from the western edge of the Iberian Peninsula and about 3,900 km (2,400 mi) from North America. Seismic activity, though rare, still occurs on occasion.
The Azores islands have a subtropical climate with high humidity and often experience fluctuations in weather patterns. Expect temperatures to range between 15-25 degrees Celsius (mid-60's Fahrenheit). Locals joke about "four seasons in a day;" rain, humid with sun, clouds, and wind all within a few hours.
The official language in Azores is Portuguese. On most of the nine islands, the variety of Portuguese spoken is similar to an archaic form of European Portuguese due to when it was discovered. Each island is an exception and has its own distinct accent. The dialect spoken by many of the inhabitants of the largest island, Sao Miguel, is where the many individuals employ a local "Micaelense" dialect  very unlike that found on the Portuguese mainland. In fact, even the people from Mainland Portugal and the other Azorean islands find it difficult to understand them at first. For those visiting the Azores on holiday, however, the good news is that most of the people involved with tourism speak at least well enough English to be able to communicate with tourists.
The main hub is in Ponta Delgada Airport (PDL). There are SATA served airports on every single island (some of them have only 1 flight daily though).
Major carriers serving the islands include:
On most islands there you can rent a car or a scooter. Please note sometimes terrain is very cloudy due to elevation, and you may be driving on very steep and narrow roads near cliffs. Many tourists prefer seeing the scenery this way, but if you are a nervous driver perhaps get a tour guide to do the driving for you. On most islands there are also bus services that run around the islands, crossing the main villages. On the smaller islands however, these may have only a few runs per day, or none at all on certain days (Sundays, holidays).
These being volcanic islands, in many places the terrain is steep and rugged. The roads wind around very steep hillsides. Cycling around the islands is possible if you are in great shape, and don't mind a lot of hill climbing.
This is a great place for going around island to island and even town to town by boat . Almost every town is on the shore and most have ports. One of the best known sailing ports in the world is Horta, on Faial Island. There is a large and fully equipped marina that has catered for many famous boats and regattas. The marina is ideally placed in downtown Horta. Some other islands have marinas, like Terceira and São Miguel. Even when a marina is not present many of the larger villages have a harbour suitable for mooring a sailboat or yacht.
You can fly between islands for a very reasonable fee by the local airline, SATA. Most islands have daily flights between them, and if you are having a whole-day 4x4 tour, you can arrange for them to pick you up at the airport.
Free flights from PDL and TER to small islands
Apparently the Portuguese law pertaining to the financing of subsidized flights to the Azores (public service option) obliges the airline that connects the minor islands with the major airports (Lajes and Ponta Delgada) to provide customers who have bought a ticket from Madeira or the Portuguese mainland to the major airports upon request one onward return flight to one of the smaller islands at no extra charge.  (The idea is that it shouldn’t be prohibitively expensive to visit the smaller islands.)
Taxis are available, but are still slightly unreliable (even if you call/email to confirm pick up, they may not show.) Taxis are readily available at the airports, and if you are not staying in a hotel, you can always walk to the nearest hotel and ask them to call a taxi for you. They are not commercialized enough that taxis are waiting outside hotels.
Lagoa das Sete Cidades, a beautiful hour glass green and blue body of water known as a caldera northwest of Ponta Delgada. It is storied with myths and legends.
Lagoa das Furnas, an active caldera with steam vents, mud pots and geysers, locals cook food in earth ovens available in picnic areas.
Lagoa do Fogo (Fire Lake) is a beautiful caldera lake high up in the mountain and known for its dramatic views and white sand beach.
At Faial Island see Horta Harbour where all sail boat stop, Faial Caldera and Capelinhos volcano.
At Pico Island you can climb the mountain, 2351 meters above sea level. It is the tallest mountain in Portugal. Idealy you climb the mountain in the afternoon so you can see the sundown when you are in the top. Normally it takes 2 to 3 hours to climb. More if you are not fit. Then in the morning to see the sunset you climb a little mountain that is called Pico Pequenino (Little Pico) that the mountain has on the top. From there you can see the islands of Faial and São Jorge perfectly.
At Terceira Island, visit UNESCO's Angra do Heroismo, a charming XVIII century little city full of local shops, cafes and bars. Terceira is inherently the happiest Island, and events occur all year long, mainly the famous "Tourada à corda" where bulls are set free in the streets in a party environment. Since the XVI century, after the Spanish every year, each street or village performs a tourada (from May to October). Get a taxi or rent a car to go to one (every day touradas are performed). Once there pick any "Tasca Tradicional" (basically, a van with a bar) and eat a bifana (hot meat sandwich) and a cold beer, then find a safe place to watch the locals dodging the bulls. Get a tour around the island, go inside a volcano (Algar do Carvão), a cave (Gruta do Natal) or walk throught any of the dozens Trilhos (official hicking trails). Praia da Vitória is the second largest city in the island and has a beautifull sandy bay, where most water-related sports are available.
Sao Miguel, fly to Faial from Ponta Delgada, take the boat to Pico Island, take a boat for Whale watching at Faial or Pico, climb the Pico mountain if you are in good shape, take the channel boat to S. Jorge and then fly to Terceira Island. In each Island the best is to rent a car (cheaper) or to hire a taxi to see around all the Islands and enjoy the views.
The Azores are known as the most self-sustaining islands in the world, and it’s easy to see why: they grow almost all their own fruits and vegetables, raise their own meat, make their own dairy products and have plenty of water. However, there is a "meat and potatoes" mentality when it comes to the cuisine and vegetables can sometimes be hard to come by.
Fresh fish is very good. There is also a large amount of cattle on the island and the local grass fed beef is very good.
The islands are famous for their cheese production. Queijo São Jorge (sharp and spicy) and queijo do Pico (younger and more buttery) are perhaps the most renowned, but each island produces several kinds and they are all good. You can find them in most local grocery stores. In Ponta Delgada O Rei Dos Queijos (“The King of Cheeses”) has perhaps the widest selection and offers samplings.
The Azores produce 30 percent of Portugal's milk: however, all of it is ultra heat treated (UHT) and fresh milk is virtually impossible to find and farmers cannot legally sell it.
Pineapples from San Miguel, local bananas, small figs and maracujas are also widely grown and available.
Bolos levedos are traditional bread rolls similar to English muffins (if you get a burger, ask for Bolo Lêvedo for the bun).
For local tea, try Cha Gorreana or Cha Porto Formoso. You can visit the plantations, too.
Sagres and Super Bock are the best Portuguese beers you can find on the island. Especial is the local Azorian beer, very good.
You can also ask for local sodas "Kima" and "Laranjada".
There is very little crime in the Azores. What little crime exists is mostly drug related. There are no reports of crimes against tourists.