The nearest international airport is in Frankfurt am Main (approx. 80km from Heidelberg). There are several options to get from the airport to Heidelberg: 

1. Deutsche Bahn: The train ride from Frankfurt am Main Airport (FRA) to Heidelberg takes about 45 minutes (https://www.bahn.de/angebot). 
2. Shuttle: The shuttle bus ride is one hour (https://frankfurt-airport-shuttles.de).

From the train station in Heidelberg it takes about 10 to 15 minutes by streetcar or bus to the old town. 

Rhein-Neckar-Verkehr GmbH is a transport company that operates local public transport services in the Rhine-Neckar region in the major cities of Heidelberg, Mannheim and Ludwigshafen am Rhein. You can buy different tickets (single stops or day ticket) (https://www.rnv-online.de/fahrtinfo/).