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 https://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.
