Some decent information on here if you are staying over in Basel or one of its suburbs:
http://wikitravel.org/en/BaselFrom the airport, visitors can rent a car, though the most comfortable ways of getting into centre are
*Taking bus 11 from the French exit to the railway station in St Louis and changing to the Basel commuter train to Basel SBB station.
*Taking the bus no. 50 from right outside the Swiss arrivals area to the Basel SBB train station. Most hotels offer a free mobility pass, which includes bus transport to and from the airport, so your printed hotel reservation might allow you free transport.
Mobility Pass: All hotels in Basel, including the youth hostel, offer each registered guest a free "Mobility Pass" upon check in. This gives free unlimited travel in Basel and suburbs (including to and from the airport) for the duration of their stay. This is easily worth the price of a lunch every day you stay. (If you have written confirmation of a hotel reservation you can also use this to travel from the railway station or airport to your hotel. At least one respected hotel in Basel advertises this fact on their web site.)