Karlsruhe lies on several high-speed long-distance train lines, for example those connecting Paris and Munich, those connecting Berlin and Zurich, and those connecting Amsterdam and Basel. Tickets can be booked online at www.bahn.de/
To arrive by plane, the most convenient airport is Frankfurt International, which is one hour by train from Karlsruhe. From within Europe, there are also many budget flights to Stuttgart airport, which is also one hour by train or bus from Karlsruhe.
Note: There will be major railway construction in October 2024. Long-distance trains will be diverted and there will be bus replacement services between Frankfurt airport and Mannheim central station. Please allow for additional time to travel to/from the airport and check for last-minute changes, see http://www.bahn.de for information.
Direct connections from Frankfurt and Stuttgart airports to Karlsruhe are also offered by Flixbus: https://www.flixbus.com/