Easy. Make small claim after claim to prove yourself.
Don't start with Ilia.
Tell them right before they encounter it what kind of power output the cloud represents.
Give Spock the hint to look for radio signals.
Tell them to answer it BEFORE Ilia gets digitized.
Tell them to communicate to V'ger about knowing the creator before everything almost goes south.
Get inside and transmit the final sequence.
if that fails, tell V'ger to assimilate Ilia and mate with Decker, as that was the only thing that satisfied V'ger anyway and tell Kirk, "Sorry, shit happens"