They overthrew their countries in the name of Allah. Atheists, or those the Qur'an calls Infidels had to convert to Islam and if they resisted, they were killed.
For Christians and Jews, well they occupied their nations and were forced to pay the Jizya, that is a tax. With it they built the Mosque of Omar that is in Jerusalem today.
Non-Muslims often had to dress in common clothes and were prohibited from riding horses--a reminder of their subjection.
And when they paid their tax, they must approach the collector with their faces down, not looking in his eyes. Again, to remind them they were inferior and in subjection. Then the collector would slap them in the face before taking their money.
In most conquered countries, the Christians usually converted after a couple generations. Then they did not have to pay the tax. Hope this helped