HI Don: There are several sorts of ground. The first is the "safety ground," which SHOULD be taken care of by the grounded "pin" connnection on your wall sockets. But it's been my experience that relatively few of those things are actually grounded. And it's also been my experience that a safety ground is not absolutely necessary for second story ham shacks because there's no way you can contact your rig and something that's grounded. So you can't become part of the ground circuit.
On the other hand, RF in the shack can be a serious problem. If your mike is biting your nose when you transmit or your audio is distorted you have an RF problem. The usual cause is a mismatch at the antenna feedpoint. The outside of the coax makes a better match to the coax than the antenna so most of the RF comes back down the outside of the shield. And what's not radiated causes trouble in the shack.
A "counterpoise," essentially a quarter wave antenna attached to the rig may radiate enough RF to reduce or eliminate the problem. That's the theory behind the "artificial grounds," avilable from MFJ and others. But that's also a bandaid solution.
The most effective cure for RF in the shack starts at the antenna. A better match where you operate is a start. Adding enough coax to make your feedline an even number of half waves long where you operate will make your coax shield "high impedance" and reduce the amount of RF on the outside of the shield. A "current balun" (see www.radioworks.com
for more info) at the antenna feedpoint can choke off unwanted RF and improve your antenna's efficency.
Running the coax through a lightning arrestor mounted on a ground rod, at ground level, with a current balun on the shack side of the arrestor will often cut RF in the shack to an unmeasurable level. A few ground radials on the ground rod will help. Another current balun between the rig/tuner and the coax will further reduce the amount of RF in the shack.
Other solutions are possible, but these should give you a start.
73 Pete Allen AC5E