You can fly to 3 main airports (Alghero; Olbia; Cagliari) served by several UK airports and many other EU countries. ryanair has an all-year-round direct route from London Stansted to Alghero. Ryanair also fly from Birmingham to Olbia (Summer only). easyJet has direct scheduled flights from Bristol & Gatwick to Olbia (Spring/Summer) and Luton to Cagliari.

British Airways and Thomson fly from various UK airports to Sardinia. During the summer season Holiday Options sometimes has flight-only availability on their Birmingham to Alghero package holiday route. There are many routes from other EU countries and mainland Italy.

skyscanner is a useful site to search for flights.

Ferries sail from 6 ports in mainland Italy, the most convenient from the UK being Genoa, Toulon in France and 3 ports in Corsica.The main ports in Northern Sardinia are Porto Torres and Olbia, and are both linked to Genoa in Northern Italy. Porto Torres can also be reached from Toulon in Southern France. There are several smaller ports linked to Corsica and other mainland Italian ports.

directferries is a useful site to identify ferry routes to & from Sardinia.