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When Standing:
As others have said, I typically use a stall for the added privacy. This is especially true when I'm using a smaller/shorter cover garment (i.e. t-shirt vs. sport coat). One technique is use is to leave the belt buckled and just undo the zipper. That wasn't something I ever did until I started carrying, but I'm finding to be quite convenient nowadays. Another option is to undo the belt and support the pistol with my hand, typically by grasping the belt near the holster or by using an open palm to press the gun against my hip. This leaves my weak hand free to take care of business. The trouble here is that it can be difficult to tuck my shirt back in with only one free hand. A slight variation on this technique is to use my elbow instead of my palm to hold the pistol in place, thus leaving both hands free.

When Sitting:
You'll definitely want a stall for this one. Beyond that, I don't have much advice as I'm still trying to figure it out myself. I'm always concerned the guy next to me will look under the divider and see my pistol resting inside my pants around my ankles. Selecting the last stall in the row (so that I have no neighbor on my gun side) can help mitigate this, but that's not always an option. Also I typically drop my pants first, then my shorts so that the latter lands on top and can be used to help hide the pistol. You can also be creative here - use a handkerchief, some TP, or whatever else you have handy to create some cover. Others have suggested removing your pistol and setting it on the back of the toilet or on top of the TP dispenser. This may or may not aid in concealment, but I always hate to unholster my gun, especially in public. (What if I drop it?)