Once you land in Louisville International Airport, you will have no trouble getting around. Downtown is 5-10 minutes away and a taxi ride will cost you about $15.  The airport is relatively small and getting trough security rarely takes more than 30-45 minutes.

There is also a bus service that runs through Louisville and connects it with the rest of the county: the TARC , the Transit Authority of River City.  Louisville does not have a subway or train.  Bus service is limited compared to many larger cities.  Expect to take taxi's for most transportation especially any trips to the suburbs and outlying areas.  Louisville's traffic is very negotiable.  Parking is also easy even in downtown.  If you plan on doing much traveling around town, a rental car may be worth acquiring.

If you are driving or you plan to take cabs during the Kentucky Derby events, keep in mind that there will be a lot of commotion and traffic, and rates are higher than usual.