When he or she can achieve a skill without being taught or catches on really quickly with minimal guidance. In terms of academically or otherwise.

And when my child loves to read, to the point I will bring them to the library every weekend

Its hard to say, different gift are discovered differently.

all of the above + desire to learn more ahead of her peers

If my child is always curious, and want to find out more.

I think when kids show curiosity it is a signal

Heard that curiosity is a big deal to knowing.

When he scores well in all tests and exams

she'll always be gifted in my eyes

Her inquisitive nature is how i tell