Players needed to get 31 kills with their weapons to get rewarded with the nuke. When launched, a siren will blare and the nuke would detonate killing every player on the map without ending the match.
In MW3, the only way to get a Nuke killstreak is to go on a 30 gunstreak. This means only kills from your weapon or equipment will be counted toward the streak. Killstreak kills, such as ones from a Chopper Gunner, Juggernaut, VTOL Jet, etc., will not count toward the 30 kills needed for a Nuke.