When to use "gern" vs. "gerne"
There is no difference between the two forms in meaning, and they are interchangeable in usage. The dictionary typically even lists them as "gern(e)" rather than as separate entries.
The original form from Old High German down through Middle High German, as Duden and others indicate, was "gerne". The form "gern" is just an example of how often the final "-e" gets dropped from German words in casual usage, and some people may consider it a little more colloquial.
The usage between the two is more of a feeling or the way it sounds in the sentence or circumstance rather than a grammatical requirement. Perhaps you want to say "gerne" to really emphasize something, or perhaps just "gern" with a sense of finality. As you become more familiar with German, you will get a better feel for its rhythm and rhyme and what sounds better to your ears. The choice is yours.
I've been speaking German for about 3 years now and I felt that I finally understood when to use either one just on account of my Sprachgefühl. Never did I realise that I say "gern" when it's not emphasised, and "gerne" more so when it is. Brilliant. Thanks for enlightening me, it's always helpful to be up to date on these sorts of things.
_Einen Bedeutungsunterschied zwischen "gern" und "gerne" gibt es nicht, auch in stilistischer Hinsicht ist kein Unterschied festzustellen - beide Formen gelten als gleichwertig._ (Quelle: http://www.spiegel.de/kultur/zwiebelfisch/zwiebelfisch-abc-gerne-gern-a-323744.html)