Unfortunately, you can't order the guard dog to attack in multi-player.
The dog will follow you around and will attack enemies within a certain radius. Once the enemy is eliminated he will return to you. If you die, the dog will attempt to make it back to you and will defend it self along the way if necessary. The dog is also meant to growl or bark when an enemy is close.
My limited personal experience of this kill-streak is that the dog does not need line of sight to attack a player. If you come into its "attack" radius, then it will try and attack. I say try, because I've noticed on a few occasions that they can get stuck or confused as which is the best route to take for the kill!
The dog will happily jump out windows and off ledges if it thinks it can defend you. This doesn't seem to hurt it. A dog can take significantly more damage than a player can, but can be stunned for short periods of time by explosions, tactical grenades or heavy bullet damage.
If a dog comes across another dog they will attack each other, but won't kill. They will continue to fight until a player kills one of them.
Best Answer
After earning the guard dog killstreak, you can activate it by pressing the same button you press to activate any killstreak. On the Xbox and Playstation, press the right arrow on the directional pad. After that, the dog will appear at your side an attack enemies who come near you.
Source: Personal experience playing many call of duty games.