Konstanz is well connected by rail, especially from Switzerland. Zurich is the most natural gateway — trains run direct and take about an hour. From Stuttgart the journey is around two and a half hours; from Munich, also roughly two and a half hours with a change. The rail connection through Switzerland means that Swiss rail passes are valid on part of the journey, and it's often cheaper to route via Zurich than to go entirely through German rail.
The train station sits at the edge of the old town, a short walk from the harbour and the main pedestrian area. There is no airport at Konstanz; the nearest international airports are Zurich (about 60km by road) and Stuttgart (about 180km).
From the Swiss side, Kreuzlingen directly borders Konstanz — the two towns essentially merge — and Swiss trains arriving at Kreuzlingen Hafen station put you within walking distance of the Konstanz old town.
By road, Konstanz is on the A81 autobahn network via Singen. Parking in the old town is limited and expensive; most visitors leave their cars at one of the car parks on the edge of the centre and walk in.