Each Canary Island has its own airport, with flights from the UK being more frequent and generally cheaper to the most popular destinations of Tenerife and Gran Canaria, but good deals are there to be found and there's never a bad time to visit. Tenerife is the only island with two airports. Though the Canaries are small enough that one airport can easily serve tourists bound for all over the island.
Public transport is fairly limited across all the islands. There is a small amount of train track in Tenerife but buses are the main form of public transport, with routes normally ringing the main roads and resorts. It's best to check with your tour operator when you book your holiday since many companies across the Canaries offer transfers included which is the easiest way to get to your accommodation. Taxis are available and generally reasonably priced.
Bus travel will allow a tour of the coastal areas on most of the islands, but to see the interior of the island there are two options. Joining a tour is a great hassle-free way to see the main sights or hiring a car will allow you to make your own way around and visit some out-of-the-way gems. Plane travel or ferries are on hand to get you between the islands if you fancy island hopping and seeing a bit more of the archipelago, but you may have a problem if you want to take your hire car with you, so check before you make plans. Plans are underway for a huge walking circuit taking in all the major islands and some parts are ready already if you want to take exploration nice and slowly.