The dominant firm is the price leader, and the rest of the firms take this price as given, and respond to it by producing at a quantity where marginal cost is equal to this price (which is also the marginal revenue for these "fringe" firms).
The graph below shows a typical dominant firm model:
The black line represents industry demand, which is the total demand for the market (ie. the horizontal sum of individual demands).
The blue MCcf line represents the marginal cost for the competitive fringe. This represents the sum of the individual marginal cost curves for each of the firms participating in the perfectly competitive side of this market.
The green MCdf line represents the marginal cost for the dominant firm. The dominant firm is the firm acting as a monopolistically competitive firm, which can choose which price (within a range) it will charge its consumers.
The purple Ddf line represents the demand curve for the dominant firm. Not that the demand curve for the dominant firm is always below the industry demand curve, and becomes the industry demand curve after price level 'F' because all competitive firms exit the market.
Finally, the orange MRdf line represents the marginal revenue curve for the dominant firm. This line has twice the slope of the Ddf line and is intuitively identical to the MR line for a monopoly or monopolistically competitive firm.
The important points to are labeled with different letters. The point 'A' represents the intersection of the industry (total) demand curve with the price axis. This is the price that must be charged for no quantity to be demanded. The point 'B' represents the price level that would be attained if there was no dominant firm. This is calculated by looking at where the perfectly competitive firms marginal cost curve crosses the industry demand curve which occurs at point 'C'.
Since anyone can acquire the good or service at the price level of 'B', this is the maximum price that the dominant firm can charge for the good. This means that the "fringe" demand curve (the demand curve faced by the dominant firm) will begin at point 'B'. The curve will be downward sloping, and will intersect the industry demand curve at a price of 'F'. Also note that the point 'F' is where the competitive fringe companie's marginal cost curve intersects the price axis (where quantity equals zero).
After we draw this "fringe" demand curve, we can derive the associated marginal revenue curve for the dominant firm. The point 'G' shows where the marginal revenue curve and the marginal cost curve of the dominant firm, cross. This gives us the profit maximizing output quantity for the dominant firm, and if we draw that line up to the "fringe" demand curve, we see that it will intersect at point 'D', which is the optimal price charged for the good by the dominant firm.
Also note that Qcf shows the quantity supplied by the competitive fringe and Qdf shows the quantity supplied by the dominant firm. Unlike traditional supply and demand graphs, the total amount of goods supplied to the market in this graph is Qdf + Qcf, not simply one or the other.