Building the demand curve
The demand curve is a linear graph (can be a curve as well) showing the relationship of price with the quantity. It is sloped with a negative gradient (sloped positively in case of backward bending curves, like the labour curve). The demand curve shows the effect on quantity demanded when there is a given change in price or demand. The demand curve is usually drawn in conjunction with a supply curve, showing the market.
Constructing the Demand Curve 
1. Draw a set of x (horizontal) and y (vertical) axes. The vertical axis is labelled with the price of a particular good; thus, this axis is often labelled "P". Similarly, the horizontal axis lists quantities of the good under analysis, and consequently is often labelled "q".
2. Plot points from a demand schedule; these should show the quantity demanded at different price levels.
You may find (for instance, on an assignment) that you are given a demand function and are being asked to plot the function. In this case you must construct the demand schedule yourself. All this requires is to choose a range of prices (ex. 0, 5, 10 . . . 100) and then enter these into the function to calculate the associated quantities demanded in the market.
Let's suppose, to illustrate, that the demand function has the following form: q = -5P + 25. You would create the demand schedule by first constructing a table with two columns, one for price and one for quantity demanded.
Then you would choose a range of prices, say, $0, $1, $2, $3, $4, $5, and write these under the 'price' column. For each price you would proceed to calculate the associate quantity demanded. For $1, as an example, the quantity demanded is 20 units (-5*(1) + 25 = -5 + 25 = 20). Write next to each price the appropriate quantity. When you have done this for all of the prices your demand schedule will be complete.
This simple function, by the way, illustrates some an important point about demand curves.
An important point to note in economics is that the independent variable (i.e., the price) is plotted on the Y-axis and the dependent variable (i.e., the quantity demanded) is plotted on the X-axis, though in mathematics the converse is usually true.
Price Elasticity of Demand 
The demand of a commodity is said to be price elastic, unitary inelastic or price inelastic by the gradient of the demand curve. Price elasticity refers to the responsiveness of quantity demand given a change in price.
A demand curve with a small negative gradient is said to be elastic. Elastic demand indicates that given a price increase, quantity demanded will fall more than proportionately, leading to a fall in total revenue [ie. price times the quantity]. A good with elastic demand should be priced low to maximise total revenue. Elastic demand tends to mean that the commodity is a luxury product, has a large number of substitutes and spending on it makes up a large proportion of consumers' income. An example would be LCD televisions.
A demand curve with a high negative gradient is said to be inelastic. Inelastic demand indicates that given a price increase, quantity demanded will fall less than proportionately, leading to a rise in total revenue. A good with inelastic demand should be priced high to maximise total revenue. Inelastic demand tends to mean that the commodity is a necessity, has few substitutes and spending on it makes up a small proportion of comsumers' income. An example would be petrol.
A hyperbolic demand curve is said to be unitary elastic, that a change in price will lead to an equal proportionate fall in quantity demanded; total revenue would remain unchanged. It is uncommon to see commodities with unitary elastic demand, and would be mere coincidence if so.