Braunschweig Hauptbahnhof is on the main ICE line between Hannover and Berlin, with fast trains roughly every half hour. From Hannover it's 35 minutes; from Berlin Hauptbahnhof, around 2 hours. Frankfurt is reachable in under 3 hours with a change at Hannover. Direct trains also run to Hamburg (1 hour 30 minutes).
The city has a small airport (Braunschweig-Wolfsburg Airport) but it handles almost no scheduled passenger flights; all practical air travel uses Hannover Airport, 50 km west, from which regional trains complete the journey in about 40 minutes. By car, the A2 autobahn (Hamburg–Berlin) passes north of the city; the A391 connects to the city centre.