first off, who is telling you this?
For proper grounding of the chassis, you need a grounded outlet. That's it, that's all. To properly ground your MB indide the chassis, well, you can't help but ground it. The 0V lines (or Ground or black wires, whatever you want to call them) are directly connected to the chassis through the PSU. So every single piece of equipment in your chassis is grounded properly. That's all there is to it.
As to anti-static protection, all connectors on your PC have to pass a static suppression test. In other words, any connection on the outside of your PC is capable of suppressing a 15kV static shock. The only time you need to worry about static is when you're working on your PC. In those situations, touch the unpainted chassis of the case and use an anti static band. It doesn't matter where your pc case is on floor or off. not on carpet though
A good place to start is your choice of clothes. Identify which clothes you have that generate lots of static and avoid wearing them when working with PC's. That applies to shoes too. Avoid moving your feet when you're working on the PC. I like to find something other than the PC to earth myself on. Plugged in PC's are good, but if you have a permanent object that you can earth on, use that too. Good to know if you're working on laptops or other devices that don't have earth through mains power. I used to touch a metal shelf behind me and my bench was also grounded. A good jolt sometimes, but it'd help discharge static.
The point of grounding yourself to the case is that it doesn't matter if it's actually at 0V or not. As long as you and your case are at the same voltage, there's no voltage difference on components, which is what fries them.