To conquer enemy territories you need to send your troops to attack them! 

How to make an attack 
To send an attack tap on one of your territories with more than 1 troop. Then tap the enemy territory to send the troops to.

War game risk attack

After selecting the target territory the troop selector will appear to let you specify the amount of troops to send.

War game risk attack

The attack algorithm does not use randomness. To win your attackers need to be slightly more than the defenders. To check the expected result tap on the 'i' button:

War game risk attack

In this example 8 vs 1 will produce a result of 7 attackers and 0 defenders left thus conquering the territory.

Multifront attacks 
If you make two attacks to the same territory at the time of simulation the attacks will happen simultaneously. In the following example there are two attacks from Algeria and Ethiopia to Egypt. At the time of simulation this attack is equivalent to doing 1 attack with 2 offensive troops. 

War game risk attack

You may stop this behaviour by turning off the "Merge" toggle when selecting troops.

War game risk attack