I second ewie.
The "normal" past tense would be I danced. I did dance is the emphatic form of the past.
For the emphatic form, you have to add the auxiliary do.
The auxiliary is inflected while the main verb keeps its root (or neutral) form.
Present simple : I do dance / She does dance, etc....
I would call "I danced" the simple past, while "I did dance" I would call the past emphatic, although some people call it the simple past emphatic. One needs that word "emphatic" in there, though, because it is obvious that "I danced" (which is the true simple past) and "I did dance" are not identical.