According to the theory, monetary growth increases inflation.
But how do companies know that there is more money in the economy now than before?
The basic intuition is that the companies either directly know by looking at what the central bank is saying, OR (and more importantly) the money growth means that money is now put into the hands of various agents in the economy. The second case is the important one.
When that money is put into the hands of various people they go out and spend that money. Thus there is increased competition to buy the same amount of goods. (More $$ chasing less goods). That competition to buy means that firms will profit by raising the price, and so they do that when they see the increase in demand.
When an everyday firm that isn't paying much attention to the central bank is thinking about setting prices, it will have two major considerations.
If a business gets more customers/orders than usual or whatnot, it has to ask itself whether or not the activity is because of an increase in real demand, or an increase in the money supply. Thus, a firm thinks about
The average inflation rate of the country. The higher it is, the more likely it is that they will misattribute real demand shocks as inflation instead, and adjust output improperly. Real demand shocks will not help the economy as much as in a country with lower average inflation.
The surrounding non-competing businesses around the firm. If other firms seem to be getting more business, and they haven't adjusted prices recently, then the firm is more likely to think of the extra business as from an increase in the money supply. On the other hand, if just the firm is seeing more business, it is more likely to think that there is a real demand shift for its products.
I would say these are the more likely ways that businesses try to parse out what inflation (and thus money supply) is like, on the aggregate level.