Have a look at this article from last year on my blog.
http://barlaventostravelblog.blogspot.com/2008/06/driving-from-lisbon-airport-to-algarve.html
If you take the toll motorway, the drive is about 2hrs 45mins to 3 hours with stops.
If you want a more leisurely drive take the motorway over the Vasco da Gama bridge and follow it till the Marateca off-ramp. Follow the signs for Grandola and the IC 1 and wind your way down to the Algarve.
Time with stops 4 hours.
