- Make your block diagram
- At each point where significant quantization can happen, add noise
- Analyze your system's behavior with that added noise
If you know that the quantization effects will be essentially random, and if the following stages tend to low-pass or band-pass filter, then model the quantization noise as Gaussian with $x_n \sim N(0, q/12)$, where $q$ is one LSB.
The justification for this is that the quantization noise will be uniformly distributed (hence $\sigma = q/12$), and the following filter's output will contain a weighted sum of a bunch of samples of the quantization noise, which will tend to Gaussian by the central limit theorem.
If you want to be Maximally Paranoid, then figure out what the worst-case behavior of the quantization noise would be for your application (stuck high, stuck low, some specific signal, etc.), and model the quantization noise as having that shape, with a magnitude of $q$. In the case of a linear system that has any frequency selectivity, this works out to a square wave at a frequency equal to the systems highest sensitivity to noise at the injection point (or a sine wave with an amplitude of $1.09 q/2$.
The justification for this is really just paranoia -- but if you have an absolute upper bound on the effects of quantization, and the system still works well enough, then you just know you're done.
To design data path widths, you can turn this around, and determine the acceptable level of quantization at each step, and make sure that your data paths are wide enough (and scaled correctly) so that quantization is smaller than your acceptable level.
It's dangerous to make general statements about nonlinear systems, but I would hazard a guess that if you can analyze the algorithm on paper at all, there's a good chance that you can analyze the algorithm plus quantization on paper.