Frankfurt International
Closest airport to me is Frankfurt International Flughafen (Airport). It has a major train station attached to it. If you don't have a car to get to/from anywhere to/from Flughaven, you go via the train.
Follow the orange train signs from your terminal to the Bahnhof (Train Station) at Terminal 1. You may need to get the train from Terminal 2.
There you will pass a DB office (Deutsch Bahn) where you purchase tickets.
Ask the nice people for a ticket to Heidelberg Haupt Bahnhof (Hbf, or Main Train Station). This should cost you $22Euro one-way. You shouldn't need a reservation, but if you do, it's only $3Euro.
The main ticket office is located approx 5 mins walk from the actual platform, you have to go up and down escalators to get there, running would have helped. I was 5 seconds late! Don't worry if you miss the train as another comes in about 15 mins during peak times.
You get a ticket and an itinerary with Platform, Time and Stations. Make note of the transfer stations where you need to get off and get on another train.
The train from Flughafen to Heidelberg requires you to:
1) Go on an ICE train Flughafen to Mannheim.
2) Change trains at Mannheim, maybe run to another platform.
3) Get on local train from Mannheim to Heidelberg
(ICE Trains are the fast luxury trains, Local trains are not as plush!)
Total time it takes from Flughafen to Heidelberg Hbf should be 50 mins (+ or - 10 mins).
General Rating: ***
Repeat Visit: *** (Would be my number 1 choice)
Frankfurt Hahn
Frankfurt Hahn is the Ryanair Airport ie. A tin shed in the middle of NOWHERE with some duty free. If you are not pushed for time and get a really cheap flight, go this way, otherwise go via Frankfurt International.
There is a bus from Frankfurt Hahn to Heidelberg - Hahn Express. This costs $16Euro one-way, you pay the driver.
Bring a book or some music. Go to the toilet before as THEY DON'T STOP FOR YOU!
(There seemed to be a WC on the bus but I think it was locked when a guy tried it. He then sprinted out of the bus when we got to Mannheim.)
The bus is a large white one, with a sign stuck to the window saying where it will be going. Don't confuse it with the Baden bus. (Hahn Express go to Baden too.)
The stop to catch the bus from Heidelberg to Hahn is in front of the Mc Donalds at the Hauptbahnhof. There is a sign so you shouldn't miss it.
The trip takes about 2 hrs, where you go through Mannheim and Worms. There is some spectacular countryside especially in Autumn where the Vineyards are turning Yellow/Orange/Red. Beautiful! So if you travel in the day you get to see that and some of the towns you by-pass.
The bus stop at Hahn to Heidelberg is across the carpark from Terminal 1 (about 40 meters). The bus stop sign has a number 6 on it.
General Rating: * (Saw some nice countryside, met a nice Melbourne girl at Hahn)
Repeat Visit: * (Would be my last resort, takes too long as you have to factor in the wait for the bus to arrive! Cheap flight though.)