Obviously, the first and easiest way to reach the Algarve is by plane. With regular flights from the UK and most European cities, the Algarve is very accessible to everyone. The best airport to fly to is Faro, alternatives within a 2-hour drive include Lisbon other options include Seville and Jerez de la Frontera in Spain.
There are direct flights to Faro from most UK airports with Ryanair, Easyjet, British Airways, Tui, BA City Flyer, Wizz Air UK and Qatar Airways. Most are reasonably priced apart from during the school holidays of course! In winter flights can be picked up for as little as £10 with Ryanair!
Other modes of transport include driving, again there are many routes for ferry crossings and of course the channel tunnel route. The ferry from Dover to Calais only takes 90 minutes, whereas from Southampton or Plymouth down to Santander or Bilbao it takes between 20-30 hours depending on the operator and starting point. The most popular carrier would be Brittany Ferries and prices range from £240-400 depending on the season.