how do i construct a valid IV, given a nonce? What does this have to do with a counter?
You may not expect this, but it depends; multiple schemes are equally secure (e.g. big endian vs little endian). Generally though the counter value is a 128 bit unsigned big endian integer. The nonce is the most significant (leftmost) part of that integer.
Furthermore, the initial low part of the counter would start at (all) zero - not one as in your example.
So you'd have:
NNNNNNNN NNNNNNNN NNNNNNNN 00000000
as starting value (as hexadecimals, where N represents some hex digit of the nonce), where the left is the most significant part. Of course this is the case with a 96 bit nonce and a 32 bit counter. This starting value is commonly called the IV.
As the size of the nonce may vary many libraries, usually the increase of the counter is done modulus $2^{128}$, with the disadvantage that an overflow in the lowest 32 bit will affect the nonce. It is usually up to the user of the AES library to test this (but you'd need $2^{32} * 16 = 64 \text{GiB}$ or almost $69 \text{GB}$ to get there).
but the same "hello world" is encrypted into something different each time
Yeah, so most likely the nonce changes every time. Either that or the key changes, or even both the key and the nonce.
