How long until someone can grasp enough of the game to win chess against casual players? A few hours, weeks or what?

It takes most people about three months to go from beginner to around 1200 assuming they're studying for an hour or so every day. A 1200 would lose more games than they win but they could win most of the time against people who don't play much. 

It would take about a year to reach 1400 (again, assuming studying everyday). 

And about another 6 mos to a year to get to 1500. A 1500 is considered an average tournament player. They should beat casual players most of the time. 

Online ratings are generally a couple hundred rating points higher than real ratings. 

One game, if the person is bright.  The moves aren't that tricky and the rest is just getting over the boredom of playing a game with unmatched players enough times.

It depends on your IQ level.

Took years for me.

What is a casual player? One can grasp the basics of good Chess in say 6 months.

But 10 years to reach my level.