How to know that I am grounded with an anti-static wrist strap?
A proper ground strap connection should show 1 to 10 megohms between the part that contacts your skin and the ground terminal of the power cord. This resistance is there to prevent electrocution through the strap.

The point of a ground strap is to dissipate static charge. A large resistor does this slowly enough to not "zap" you, but also doesn't turn you into a large ground rail yourself.