I usually spend about four weeks on this material in class so even though this is an abbreviated description, I will do it in parts.
Remember that the point of any model in economics is to present a simplified version of reality that contains essential elements and strips away a lot of the complicating detail. We do this because it provides useful insight into the real world even though it may not mirror it exactly. The 'art' of economic analysis is to understand which models are relevant to each real world situation and what information is useful to extract from those models. A frequent reference point is to Newtonian physics which helps make sense of the physical world that surrounds us even if not perfectly accurate due to the simplifying assumptions.
Which brings us to the process of building an economic model which always begins with a set of assumptions. So here are the assumptions behind the model of perfect competition.
ASSUMPTIONS (MARKET STRUCTURE)
We start by assuming that there are many firms and that entry by new firms and exit by existing firms is 'free,' or that there exist no barriers to such entry and exit. We assume all firms are 'small' in the sense that any output they put on or take off of the market has no influence over the market equilibrium price. We also assume that they all produce identical products. Finally there are some implicit assumptions: that information is full and symmetric and that there are no externalities - that all of the relevant costs and benefits of this economic activity are born by the participants in the market (a counter example is if the production of the product produces harmful emissions that are born by residents of the area of production but not paid for by the firm).
You might already be wondering if this description fits anything at all in the real world. The short answer is no, it doesn't. Some markets come close and a typical classroom example is one of small family farms all producing the same kind of wheat and taking their harvest to the local grain elevator where the market price is posted and they take it or leave it. But even here there are real, if minimal, supply effects, externalities and potential quality differences. Another example is retail gasoline and gas stations as studies have shown that even a little competition keeps prices low.
So what we have is an abstraction of the real world that doesn't quite describe precisely any real world market. So why study it? Because lots of markets come close and by understanding the extremes (monopoly is the other) we begin to understand both the power and limitations of free markets.
Obviously there are two sides to every market: demand and supply. Demand comes from all of the people out there who have some desire for the product in question (and as an aside, when talking about a market we always define it for one product). People have different levels of desire for the product (and for multiple units of the same product), have different incomes, wealth, etc., meaning that they all have different levels of "willingness to pay" or "reservation prices." Willingness to pay is simply the most you would be willing to spend on a given unit of a product which is the same as the dollar amount of satisfaction you would get from consuming the product. By assumption if you can find a product being offered at a price that is lower than your willingness to pay, you should buy it and consume it and you will be better off. This is also why it is called reservation price, you would not be willing to purchase it for anything above that price.
For example if you are hungry and a slice of pizza is worth $3 to you and you find a place with $2 slices then, by purchasing it and consuming it, you are a dollar better off than you would have been if there were no pizza available. You traded $2 for $3 worth of satisfaction.
When you add up all of the people who have some demand for a product and their reservation prices, you get a market demand curve. It is downward sloping on a price - quantity graph because at high prices there may be only a few people willing to purchase but as price gets lower you add more and more people to the mix (and more people willing to buy more than one).
Next time: the supply side, equilibrium and efficiency.