Here's a breakdown of the translation:
* Je: I
* vais: go (in this context, it means "am doing")
* bien: well
Other ways to say "I am fine" in French:
* Je me porte bien: I am well (literally "I carry myself well")
* Ça va: It's going well (informal, equivalent to "How are you?" in English)
* Je suis en forme: I am in good shape
* Tout va bien: Everything is going well