What is the best way to mass produce science modules in Factorio?

In addition to the general concept of using parallel assemblers, one hint is to pay attention to the tooltip info on fabrication time for each product, in conjunction with how many of each input resource are required. Science is a little bit special (in that the consumption rate can vary depending on what you're researching), but the intermediate products can be balanced pretty precisely.

The key to optimizing for throughput (product per unit time) is properly balancing input/output ratios and also making sure your inserters/belts have sufficient bandwidth for the product flow. Sometimes you're best off inserting directly from one assembler into another as there are tech bonuses that make this more efficient (one inserter can transfer multiple units per cycle.) This is especially true for intermediate products like copper wire, where you have a particular throughput that you always want to feed directly into making circuits. Speaking of which, you're going to want a lot of circuits, so when you design your layout, keep some space available for expansion.

When doing this balancing, consider that higher assembler levels give bonuses to cycle time, meaning you might need to tweak your balancing as new technologies improve efficiency. Later in the game, you can also consider using modules to further optimize your production line.