First of all, we need to look at the possible situations in which firms may find themselves in the short run.
With each of the three diagrams above, the situation for the firm is only drawn. The 'market' diagram, from which the given price is derived, is the same every time, so I've missed it out. The main thing is that you understand that the prices P1, P2 and P3 are determined by market demand and market supply. Also note that in all three diagrams, the MC curve cuts the AC curve at its lowest point. Look back at the 'Costs and revenues' topic if you don't remember why.
The three diagrams show the three situations in which a firm could find itself in the short run.
In the top diagram, the given price is P1. The firm wants to maximise profits, so it produces at the level of output where MC = MR. This occurs at point A. Drop a vertical line to find the firm's output (Q1). At Q1, AR > AC and the difference between average revenue and average cost is the distance AB. This is the profit per unit. To find the total super normal profit, we must multiply the profit per unit per the number of units. In the diagram, this is the area ABCP1 (the red box).
In the middle diagram, the given price is P2. In this case, it is clear that the firm will not be making a profit. The AC curve is above the AR curve at all levels of output. The firm will still want to minimise its losses, though. This can be done, again, with the trusty old formula, MC = MR. This occurs at point D giving output Q2. At Q2, AR < AC and the difference between average revenue and average cost is the distance DE. This is the loss per unit. To find the total losses, we must multiply the loss per unit per the number of units. In the diagram, this is the area DEFP2 (the red box).
In the final diagram, at the bottom, the given price is P3. Again the firm will produce the level of output for which MC = MR. This occurs at point G, giving a level of output of Q3. Notice that at this point, AR = AC, so the firm is making normal profit.
So, in the short run, a perfectly competitive firm could be making super normal profit, or a loss, or just normal profit, depending on the given market price. Note that if the firm's losses get too big in the short run (i.e. AR < AVC) then it will have to shut down (see the section above).
The two sets of diagrams below will help to show that in the long run, all firms in a perfectly competitive market earn only normal profit.
In the diagrams above, the initial price is P1, due to the fact that the initial demand and supply curves, D1 and S1, cross at point C. This given price means that each firm's demand curve is D1. MC = MR occurs at point A. AR > AC, so each firm is making super normal profits. But what will happen as we move towards the long run? Remember that there are no barriers to entry or exit in a perfectly competitive market. This means that new firms will be attracted, in quite large numbers, into the market. This will increase market supply, shifting the supply curve to the right. This will keep happening until the given price is such that all firms in the market earn only normal profit. All of the super normal profit will have been competed away. Once the supply curve has shifted all the way to S2, with a given price of P2, then every firm in the industry will be earning normal profit and there will be no incentive for any firm to enter or leave the industry. This is, therefore, the long run equilibrium.
In the second set of diagrams above, each firm is making a loss at the initial price P1. MC = MR occurs at point F, where AR < AC. As we said earlier, firms can take a reasonable sized loss in the short run, but this is not sustainable as we move into the long run. Again, there are no barriers to exit, so some firms will leave the industry, causing the market supply curve to shift to the left. This will keep happening until the given price is such that all firms in the market earn only normal profit. Once the supply curve has shifted all the way to S3, with a given price of P3, then every firm in the industry will be earning normal profit and there will be no incentive for any firm to enter or leave the industry. This is, therefore, the long run equilibrium.
Notice that I haven't drawn a set of 'long run' diagrams for the situation where firms earn normal profit in the short run. This is because nothing happens. If firms are earning normal profit in the short run, there is no incentive for any firms to leave or enter the industry. The diagram stays the same so that the long run equilibrium looks the same as the short run equilibrium.
It is also important to note that, in the long run, all firms in a perfectly competitive market are both allocatively efficient (because price = MC) and productively efficient (because at the equilibrium output, MC = AC). In the topic on 'Market failure', the fact that a market has not failed if it is efficient in both these ways was discussed.