Basel has its own airport, the Euroairport Basel. A shuttle bus will bring you from the airport directly into the city center of Basel. An alternative option would be to fly to the much larger airport in Zurich and then travel to Basel by train (1 hour).
Basel lies at the border to France and Germany. It offers excellent train connections all over Europe. The Swiss trains are very well known for their punctuality and offer a relaxed way of traveling.
Traveling to Basel by car is feasible, however, parking lots in the city center are expensive.