The item gains stacks as you participate in champion kills and in damaging jungle creeps. I still have to test a little, but I believe you need to auto a monster at least once to get the stack, as smiting it did NOT increase my stacks (possible bug also).
Once you make it to 30, you get sated devourer. This makes it so that every other attack applies on hit effects. To the best of my knowledge, this does NOT mean it is a second attack. Therefore, it should still take 3 auto attacks to kill a ward, but I would need to test to be sure (I usually play shyvana jungle, so auto Q kills the ward, which is why im not sure if sated devourer usually takes 2 or 3 hits).
Because it is applying on hit effects a second time, any abilities that rely on counters come up every two attacks instead of every three. For nocturne specifically, I believe the only benefit from a kit perspective will be reducing the cooldown on your passive at a faster rate (because basic attacks on hit reduce the cooldown of the passive by one second) or at least this is my understanding of the item.
Items are affected in similar ways. Botrk will apply twice on the mirrored attack, gunblade cooldown will be reduced by 6 seconds on the attack instead of 3, rageblade (does that item still exist?) will give 2 stacks per mirrored attack, nashor's tooth will double proc, etc.
All in all, nocturne probably isn't the best champion to build devourer on. It works better on champs that have on hits built into their kits.
For example, Xin's heal comes up much more often. Udyr's pheonix form would proc after 2 attacks. Shyvana benefits immensely, the damage from her W is double proced, as well as her % max health damage. Irelia's true damage would be doubled, and then of course there is the biggest offender in master Yi, who basically has the sated devourer ability as his passive already (although his second attack on his passive deals damage as well).