より indicates a comparison rather than a superlative. In AよりB you are describing B with A as a reference. e.g.
AよりBがいい。
Compared to A, B is good. = B is better than A.
AよりBが高い。
Compared to A, B is tall. = B is taller than A.
AよりBが好き。
Compared to A, B is liked. = I like B more than A.
In your sentence your making a comparison with だれ (who). So you get:
ぼくはだれよりかのじょがすきなんだ。
For me, compared to who, the girl is liked.
Now that translation is obviously nonsense, but I hope it isn't too much of a leap of the imagination to see how that would become:
I like the girl more than anyone (else).
Where だれ ends up with the meaning of 'anyone' rather than 'who'.
As for the なんだ ending, this is an example of the 'explanatory の'. There are loads of questions about that on this site. Have a browse.