There are several ways to travel from Hamburg airport to Borgwedel.
Best and easiest would be to rent a car at Hamburg airport. In this case you are also more flexible during the event.
But it is also possible to come by bus / train. In this case you should get to "Schleswig" train station (10km from Borgwedel). From there we will arange a shuttle. Or taxi can be used.
Directly from the Airport there is the "Kielius" bus: https://kielius-onlinebuchung.de/
Tickets can be bought online or directly on the bus.
The bus will stop at "Neumünster" train station (half way to Schleswig) from where you can take a train to "Schleswig"
For all other options you have to get from Hamburg Airport to Hamburg main train station first.
With the Flixbus https://global.flixbus.com/ you can get from Hamburg main train station to Schleswig.
Or from Hamburg main train station you also can take a train to Schleswig.
Within Hamburg you can travel with public transport: https://www.hvv.de/en
For getting from Airport to main train station you should take the train "S1".
Tickets can be bought online.
Tickets are also valid for use on some ferries in the harbour area (maybe an option if you spend some days in Hamburg).
For all trains you can find information here about tickets and timetables: https://www.bahn.de/en