There is good news and bad news when it comes to driving in the Algarve. The process of getting started can be a tough one. This article will hopefully answer a few of your questions.
Bringing a car from the UK to Portugal - If it's just for a holiday, no problem. Just be sure to observe the differences in the law, the road system and try to remember to drive on the right.
If however you wish to bring your car to live with you, that is a different can of worms. You must matriculate the vehicle (re-register the car to Portugal) which is very expensive. This is a subject many people are watching closely. Technically Portugal is breaking EU law by imposing this condition, after all the whole idea of the EU is being able to buy anything in Europe and use it anywhere in Europe. The EU have told Portugal that they should stop this, but have lately chosen to ignore that it is going on. So with that in mind, you would be better off selling your car in the UK and buying another here. That way you bypass the expense and may kilometers of red tape and you'll have a car with the steering wheel on the correct side.
Buying a car in Portugal - this is a fairly simple process similar to what you are used to. Cars here , due to the difficulty of importing, are quite expensive. Once you have found your chariot of choice you must register it to your name. This will cost you about €70. Now for the good news. Cars are cheap to run once you own one. The tax is a fraction of the price of UK road tax and the insurance is cheap and includes full relay breakdown cover, wow. Not only that, there's more, this insurance covers the car, so anyone can drive it with your permission. There is a annual test similar to the MOT called inspection.
Driving in Portugal - There are a few things you need to know, good and bad, about driving here. The Portuguese are a wonderful, friendly people who love to share their food and culture with you. But they are chilled out race of drivers, they favor an aggressive posture with little patience. One habit that will shock you is their love of driving bumper to bumper with you at high speeds while trying to pass you on either side while talking on the phone and smoking. If you remember to drive is if everyone else is trying to kill you, you'll stay safe. The good news is, the roads are not crowded and you will hardly ever be in a traffic jam. There are no UK style "cash cow" speed cameras lurking around ripping you off with a fine every time you go over the speed limit by a couple of ticks. The scenery is beautiful and the weather is good for driving.
Alternatives - Car hire is very reasonably priced with most companies allowing you to collect a car from the airport and leave it at you choice of location in the Algarve and vice versa. Public transport is good. Bus, coach and train trips are very cheap. Taxis are located in central ranks in most towns.