Perfect competition is the state that there are many firms selling homogeneous product,so neither the seller nor the buyer can control the price.Both parties are the price taker.
In short run,it is possible for the firm to make a profit.The price is determined by the intersection point of the demand and supply curve.Since the market price is fixed.AD curve is representing the MR curve.When MR=MC.the profit will be maximized.
Not all the firms are making profit in short run,some be just at the break even point,some even suffer from a loss.Depends on the position of their short run cost curve.
However,in long run,the profit enjoyed by the firm rarely maintained.Because there may be some new firms entered into the market.Thir entry will lower the price and shift the demand curve down.Finally,the demand curve will touch the AC cuve at its lowest point.And leading the firm to make zero profit.
My explain may not be so clear enough..
This topic may really take you some time and effort to understand...
Hope it can really help you :-)