Attacking has to be done by clicking the globe symbol to get to the map.
The globe will rotate towards the region to be attacked.
Click on the flag icon to get the mission detail popup.
Click on Scout to scout the region before attacking.
While scouting you can check out the buildings, their levels and range. You will also see how much loot is available. You can click on attack to start attacking.
While attacking the buttons to place troops and to call air support become available. The progress of how much of the base is destroyed is displayed. Also a timer appears that tells when the battle auto-starts. Attacking yourself will start the battle.
First it's best to call air support on Defenses using Command Points. If you destroy all defenses your enemy can't retaliate and kill your troops. When calling air support everything around will be damaged or destroyed. When buildings get destroyed your command points will refill.
Afterwards you can deploy troops and let them finish the mission.