During the start of the mission you'll be taking control of a chopper. Guide it around and take out the various targets that Hudson points out to you. Eventually an enemy chopper will appear, and you'll need to blast it out of the sky with your missiles.
Even if you manage to win the fight, the enemy chopper will do a brutal amount of damage to you--much more than you can repair--as you come crashing down, aim for the ship's helipad so you can make some what of a landing.
Now on the ground, the first wave on enemies and grab the dropped rocket launcher. Use this to lock on and destroy two more helicopters that emerge before moving deeper across the ship.
Inside, follow Hudson and kill anything that gets in front of you. Hudson and Weaver will give you great support but you'll still need to help support them and get in your own kills.
Swim up the next area and arm yourself with the guns in the room. You may be hurting for ammo after the last section, so a fresh weapon will help out oodles.
Kill more guards and be sure to steal their items if you are running low. Be sure to move to rooms and around corners carefully, as the guards will try to get the jump on you or even charge with melee hits.
Move up the last ladder and out of the flooded areas and you'll soon come to the big bad main enemy.
Follow the quick time event to kill the last boss and follow Hudson. Swim to the surface and watch the ending of Call of Duty Black Ops. Stick around after the ending as you'll gain a new Zombies mode for multiplayer.