How do you plot a complex number in an Argand diagram?

Argand diagrams are, like graphs, a visual representation. Instead of representing an equation though, Argand diagrams represent numbers.
Any number can be represented on an Argand diagram, be it real, imaginary or complex. Mostly, though, it is used to show complex numbers.

As you probably know, complex numbers are made up of a combination of real and imaginary numbers. For example 3+2i. 
An Argand diagram has two axes, like a regular cartesian graph. However, in this case the horizontal axis represents real number, just like an ordinary number line you learnt about in primary school. The vertical axis represents imaginary rumbers. The axes cross at zero, again just like in a cartesian graph.
To plot 3+2i on an Argand diagram, you plot the point where the value on the real axis reads 3 and the value on the imaginary axis reads 2i. Then, extend a line from 0 to the point you just plotted. That line is the visual representation of the number 3+2i.

Some other properties are represented by the line on the Argand diagram. The length of the line represents the modulus of the number: √(3²+2²) = √13
The line also forms an angle with the positive side of the real axis. This angle, measured in radians, is known as the argument, and is important when representing complex numbers in polar form. For many aspects of dealing with complex numbers, this form can be a lot more useful.

So you can see, just from one line on an Argand diagram, you can learn a lot of the information you need to manipulate a complex number.