Hot Springs sits about an hour southwest of Little Rock, the nearest major airport (LIT/Bill and Hillary Clinton National). The drive in is straightforward on US-70 or Interstate 30 then US-270; there's no train, and bus services are minimal. Most visitors arrive by car, and a car is essentially required once you are there — the city is spread out along the lake corridors.
The small Memorial Field Airport (HOT) handles only general aviation. Renting a car at Little Rock and driving is the standard approach.