From what I have read in Islamic history and recording accounts of the follows of the Prophet Muhammad, there were rarely any enforced conversions.
The invitation of conversion was sent by messenger to the corresponding ruler, if they refused the invitation then they would confont each other - usually on the battlefield.
But like pointed out in a previous post, people who didn't convert were allowed to stay as they were but would have to pay some kind of tax.
Islam spread very quickly in its first 100 years of conception (1400+ years ago) and rightly so as they proposed and upheld many more rights then other religions did at the time.