A DC micro-voltmeter
Here are the pitfalls as I see them: -


The connection between two dissimilar metals is called a thermocouple and this can produce a voltage of several micro volts per degree centigrade. This is why thermocouple amplifiers use cold junction compensation and they are rigorous about this. Getting an accuracy below 0.1 degC is almost unfeasible. Note that I said accuracy and not resolution.
The best DC spec op-amp I use (and I do use some pretty good ones) has an offset voltage of typically 5uV. This represents an error in your measurement system and there's very little you can do about it except perform very exact calibrations quite often.
There is also a temperature related drift with this offset too so a stable environment is important
Amplifier bias currents can play havoc with DC voltage measurements if the source (the thing to be measured) has a significant output resistance. For instance a strain-gauge bridge as a resistance of typically 350 ohms in a lot of applications and, if you choose an amplifier (or op-amp) that has a bias or offset current of 10 nA you get an offset error voltage of 3.5 uV. Clearly for measuring sources that have a much higher resistance you have to choose amplifiers with much lower bias currents.


So, my advice is look at what is available and set your requirements to be achievable. I'm not going to give you diagrams because they have IP value and this is a free advice site.