That is really a horrible schematic. They should at least have used a different ground symbol for the virtual ground. It's actually a completely different net from ground. And it looks like they used a resistor symbol for the rheostat-connected trimpot.
Such a schematic will have no (useful) connectivity information and using it for board layout will be a bad idea.
So, connect all the virtual ground 'ground' modes together, and the other 'microcontroller ground' nodes together. If you are pouring a ground plane it should be virtual ground in the analog section and microcontroller ground in the digital section. Adding bypass capacitors, though typically a good idea, will probably cause problems with op-amp oscillation in this particular 'design'.
The pot can only adjust the output voltage lower than 2.5V, down to the saturation of the op-amp. Since the 3140 output will swing from a couple hundred mV up to Vcc - 2V or so, it is asymmetrical too.
They show the wiper on the trimpot connected to +5 through a 1M resistor, and one of the ends of the element goes to R5/C2/R2 etc. Either end will work, it will just reverse the effect of pot rotation. Tie the otherwise unused end of the element to the wiper, not as shown, for a bit better design.
Okay, I got a clear idea of how this works after some research. Here's help for those who need it in the future.
The Opamp in the bottom half of the image actually produces a voltage of 2.5V when connected with an Arduino.(5v) The output of the second Op-Amp, therefore, is the Virtual ground. All connections labelled as virtual ground must be connected to the pin 6 of this Op-Amp