1) There is no train service between Faro, Faro Airport and Huelva.
2) In summer, there may be a privately operated bus service between Faro and the Costa de Luz/Huelva but at present details are not clear.
See: http://www.transfershuelva.com
3) Depending on what time you are arriving, there are three bus services per day by bus from Faro Bus Station. You would need to take a taxi from Faro Airport to Faro Bus Station. (10 minutes) € 10.00 & bags.
Have a look at the following page on Cubsur's site which will give you more info on the bus times.
See: http://thomasallen.home.sapo.pt/travel/001.htm
One way ticket presently in the order of € 12.00
4) Transfer/Limo Service
This would cost in the order of € 130.00
One company that offers this service is:
See: http://www.low-cost-transfers.com/faro-airport
5) Taxis
Faro Airport 2008/2009 winter guide is quoting between € 113.00 and € 140 for a 4 person cab - Faro Airport to Huelva. Be aware there are likely to be extras.