How do firms in a perfect competitive market compete? Watch
Perfect competition is unlikely to exist in real-world markets. Firms do essentially 'compete' as they have the objective to profit-maximise. Costs can be different, but all firms will make normal profits through (P/AR/MR = AC) in the long run, because if firms are making supernormal profits, new firms are encouraged to enter the market through the profit motive. This causes market supply to shift outwards, reducing the market price until (P2/AR2/,MR2 = AC), as firms are price-takers.
Yes, in the long run, firms will always be making normal profit because of that reason. It's not 'competing' as they cannot manipulate price/differentiate their product, and can only hope for profit-maximisation, which always results in normal profits in the long-run.
They can compete by using a superior marketing message. Coca Cola, for instance, have done far better than the vast majority of purveyors of flavoured sugar water, and it all comes back to the brand. It even tastes pretty similar to much of the cheaper competition.
Coca-cola are however, an oligopoly firm. They are not in perfect competition as they have relative price-setting power and have large barriers to entry. Perfect competition results in no product-differentiation and no marketing.