The principle is quite simple.
You start with an error budget. If you want the last digit of a 4 digit (9999cnt) meter to be accurate, then you have a 100ppm error budget.
Then you make a list of all errors. Initial tolerances, changes with temperature, expected temperature range your device must be accurate, effects of temperature on opamp bias/offset currents, etc.
The static errors such as the initial tolerances of voltage references and resistors can be calibrated out.
Others can be reduced by for example adding a heater to get your device at a steady (above ambient) temperature.
Keep in mind that leakage current for semiconductors increase exponentially with temperature!
Sometimes you can partially compensate for some of these errors.
Then you have to divide the error budget over the parts you are using. some of the error sources may be intrinsically small and can be neglected. Other error sources may totally dominate the total error budget. You have to find a way that the sum of all errors keeps within your budget.
There is also a very big difference in what you want to make. If you want absolute accuracy then you design differently then if you are mostly interested in relative changes. A good metrology ADC is not the same as a good audio ADC.