The equilibrium quantity produced by a monopoly firm is determined by using the firm's marginal revenue and marginal cost curves. The firm will always produce (in order to maximize profit or minimize loss) at the quantity where marginal revenue equals marginal cost.
For a monopoly, the MR curve is not the same as the demand curve (it is the same for firms in perfect competition). Instead, the demand curve is somewhat to the right and above the MR curve. To find the equilibrium price, one goes straight up from the MR=MC point to the appropriate point on the demand curve. The price at that point is the equilibrium price.