Use the Demolition Tactics to destroy the Missile Silo at the beginning of the battle (usually from 3 to 5 Demolition Tactics).
Use the Sabotage Tactics to block the Missile Silo
Use Generals, heavy tanks and tanks and deploy away from the rest of your army. The generals and tanks will be targeted whilst your main army continues with the battle.
Use the Air-crafts and Destroyers to destroy firstly the Missile Silo.
Since the Missile Silo will try to target the area with the highest HP unit, it is advised that you should keep some distances between your tank units and all the other units. Remember to keep an eye on the tank units and see if they have entered the minimum valid range (red circles) of the Missile Silo.
Once your army is on the battle field, using the Assault Rally tactic on the Missile Silo can help your army destroy it quicker.
Bury the silo in a maze of walls (not placed on side of the map) to prevent attackers from taking it out easily. Don't give commandos access via gates to the silo, forcing them to go through walls to get to silo.
Avoid placing it close to the Town Center since it would grant them a double win. This one would force the attacker to choose either to go for the town center or silo
Put the Anti-Tank guns, Land Mine and Bunkers next to the Missile Silo to protect it from tanks.
Put the Air Defenses and S.A.M Battery next to the Missile Silo to protect it from planes.
Because it costs oil to use Big Red Button, make sure the buildings destroyed are worthy.
It is better to use it on Enemy's high level Defensive Buildings. Most of them are instantly destroyed.
If the target isn't something strong, you can always skip using it.
The missile also doing splash damage to the surrounding buildings and troops with lower damage. So you can also wait the moment the enemy's defensive troops pass by the target before launching the missile to destroy it all together.