The rainbow attacking method is very popular and effective. It gives a lot of advantage to the attacker in winning the battle. It is just a simple method yet very powerful.
The process of rainbow is simply send 1 type of every troops along with the archers.
An example of rainbow could be:
1 worker
1 warrior
1 pikeman
1 swordsman
1 cavalry
60000 archers
1 cataphract
The main reason behind this is to form a shield to protect the most powerful troops, archers.
How does just one of each troop form a shield for all those archers?
Battles are fought in rounds. In each round the defender and attacker try to kill each others troops. This battle takes place by single troop type. So for each type of troop you send you will get a extra round of firing. This can be simulated as follows
Suppose the defence (your opponent has 10000 AT)
So, the battle will be fought as follows.
Round 1
Enemy - The 10000 Archer Towers hit your 1 worker (remember in each round all of them hit a single type of troop).
You - Your 60k archers kills 2000 AT's(Archer Tower)
Round 2
Enemy - The 8000 AT's hit the kill 1 warrior.
You - Your 60k archers kills 2000 AT's
Round 3
Enemy - The 6000 AT's hit the kill your 1 Pikeman.
You - Your 60k archers kills 2000 AT's
Round 4
Enemy - The 4000 AT's hit the hit and kill your 1 swordsman.
You - Your 60k archers kills 2000 AT's
Round 5
Enemy - The 2000 AT's hit the hit your 10000 archers.
You - Your 50k archers kills 1500 AT's
Round 6
Enemy - The 500 AT's hit the kill your 500 archers.
You - You kill the rest of the at's.
Though the above process is very much simplified to give you an overall idea of the rainbow method. The opponent's level of research, level of walls, speed of different troops make a great difference. Sending the rainbow alone does not ensure you will win the battle, but sending rainbow troops are much better that sending only the archers.