So how does this work? Like a monopolist which has to lower their price to sell more, because a monopsonist is the only buyer of a good, in this case low skilled workers, if they want another one they have to increase the wage offered. For example, suppose Wendy's is offering a wage of $5/hr and this induces one worker to go work for them. If Wendy's needs two workers they need to pay the next worker $6/hr to get her to come work for them. But if wages are set at the margin, that is there is no way for Wendy's to pay the first worker $5/hr and the second $6/hr, then if they want two workers they will have to pay each of them $6/hr. There are several reasons why price discrimination i.e. paying one worker $5 and another $6 might not be feasible, such as bad employee morale due to perceived unfairness, the high time costs of posting two different wages and then interviewing workers one at a time, labor laws about equal work, equal pay etc.
So if Wendy's wants two workers and has to pay each worker $6 their total costs do not go up by $6 per hr when they hire another worker, but by $7 per hour. $6 per hour goes to the second worker and then an extra dollar per hour must be paid to the first worker, who would have only earned $5 per hour if the second worker was not hired. Below is a chart that with some hypothetical numbers.
The quantity of workers is in the first column, the wage (marginal cost of the next worker) is in the second, the total cost of workers is in the third, and then the change in the total cost of workers is in the fourth column. Notice that the change in the total cost, MTC, is always greater than the wage after 1 worker. This is because like in the example above, if Wendy's wants to hire one more worker it increases the wage for all of the previous workers. So when Wendy's goes from 2 workers to 3 workers, the wage goes from 4 to 6 and the total cost goes from 8 to 18, a change of $10/hr, greater than the $6/hr that would be paid to the next worker if they could just pay him $6 and keep the previous workers wages the same. This is because they pay the third worker $6/hr and have to increase the pay of worker 1 and 2 by $2/hr each (6+2+2 = 10)
So how can a min. wage increase employment in this scenario? Let's put this information in a diagram.
Here we have a demand curve for workers (the downward sloping black line), a marginal cost of the next worker curve (the upward sloping blue line), and a marginal total cost curve (the upward sloping red line). If Wendy's could pay each worker their own marginal cost, they would hire workers where the blue line (MC) intersects the black line (their demand for workers). This leads to an equilibrium quantity of 5 workers and a wage of $10 paid to the 5th worker.
But for the reasons given above, if they have to pay each worker the exact same amount as the last worker hired, Wendy's will care about the change in their total cost, and instead will hire workers up to the point where the red line (MTC), intersects the black line. This leads to an equilibrium quantity of 3.4 workers and a wage of $6.80/hr. The wage at an amount of 3.4 is the wage that comes from the blue line, not the red line. Remember the red line represents how much total costs are changing and the blue line represents how much the workers actually get paid. The reason they don't line up is because of the monopsony power of Wendy's. Because Wendy's has to pay more for an additional worker they create a wedge between the wage and how much their total costs increase with each worker.
Now let's talk about the min. wage. Without monopsony power the last worker, in this case the 5th, would have been making $10/hr. But suppose the govt institutes a min. wage of $11/hour. This is represented by the orange horizontal line in the diagram. So if Wendy's is forced by law to pay each worker at least $11/hr, they will hire the amount of workers that corresponds to where the min. wage line intersects their demand line for workers. This is at a quantity of 4 workers. So the min. wage amount of workers is 4 and the monosopny amount of workers is 3.4. This is how, in theory, a min. wage can actually increase employment. Under this scenario there are more workers (4 > 3.4) and they are all earning a higher wage ($11 > $6.80) than under the monopsony scenario.
This doesn't seem to be the case in the real world though. There are a lot of different buyers of low skilled labor. Fast food restaurants, car washes, bar security, retailers, etc. In a world of so many different buyers it is more likely that the wage for low skilled labor is set by the market demand, that is the demand of all firms who hire low skilled workers, and then each individual firm takes this price as given. That is, each firm knows that if they want a worker of a given skill level they can pay the market wage and get as many workers at that wage as they want. So if Wendy's wanted a new cashier and they are paying the current one $9/hr they can go hire another one for $9/hr if they wanted to, not $9.50 or $10.
Hopefully this wasn't too difficult to follow. Now if you hear anyone talk about monopsony power and how a higher min. wage can lead to more employment you will have an idea of how it works.