As Jennifer said, Time and feel are the principle ingredients to a good walking bass line as the harmony can be as complex or as straight forward as you like (I was bass tutor at Salford Uni for eight years so I've tried to teach alot of people to swing) Its quite difficult to swing effectively on electric as the generation and decay of pizz notes on upright lend themselves to a forward motion feel (which is everything in swing) due to the fact that in order for the note to speak in the right place, the pluck needs to be ahead of the beat a fraction, this is harder on electric as the response is so much quicker. It can be done, but I don't know many bass players who really pull it off well.
As for the harmony, It's a lifes wok and is a never ending challenge (wich is why I love it) Get a real book and learn to make simple lines that convey the sound of the changes well (there is swing to be found in the notes as well) be really simple at first but be sure that the song is being served well. Roots, fifths, thirds and sevenths are a good staring point as they have the strongest flavour of the chord in them, as your ear accustoms to the movement and you learn the chord sequence (which is crucial) you will begin to hear passing notes that link and longer lines that work through the changes.
Of course the very best way to learn lines and note choice is to listen to the millions of great recordings that contain walking bass, I love Ray Brown, Sam Jones, Scott La Faro, Dave Holland, Paul Chambers, Ron Carter..... the list goes on and on. These guys are all masters of the genre and have encyclopaedic harmonic structues mapped out in their heads which is what you need to be ANY good at this.
Jake