Question

How did the cold war begin and what weapons were used to fight this war?

Answer 1

WWII- started after WWII due to differing idealogies, actions and inactions during the war

now, weapons used is a bit trickier.
There were no real weapons actually used for the cold as there were no real engagements between the USA and USSR. It was generally fought through proxies wars (we give money and weapons to two factions in a country and have them fight it through).
If you consider threats and spies as weapon, then i would say those were the real weapons of the cold war. However, the Cold war was more of a mexican standoff in which both sides had the capability of annihilating all human civilization.