Where can I find information about how to implement IIR filters on micro-controllers?
Here are 3 points that you must consider : 

1 - What is the minimal latency you can tolerate? This is important, as it's important to know whether to need process every sample as fast as possible or if you can perform batch processing which is typically more efficient but creates latency .

2 - No matter if you implement the IIR in fixed-point or floating-point, it is always a good idea to split the filter in sub-filters. This minimizes quantization issues that can occur even if you use double-precision arithmetic. One effective strategy is to cascade the filter in second-order sub-filters. Check out https://www.mathworks.com/help/signal/ref/sosfilt.html

3 - If you implement in fixed-point, it is a good idea to create a fixed-point model in Matlab/Python/Scilab/tool of your choice and compare it to the "ideal" floating-point filter before implementing it in your microcontroller.