You can read the theoretical material following the link: [link]
Now let's see where I am using Blending Modes practically.
Multiply - is used to quickly create basic color shades. The object is filled with gradient containing shades of gray. This may be a Gradient Mesh as it is shown in the figure below.
On top of this object, there is created a new object that has the same shape. This object is filled with the basic color.
Now set the Multiply Blending Mode for the top object in the Transparency palette.
As you can see, we do not have to mix colors to get shades of the basic color.
Screen - black objects become transparent with this Blending Mode.
Darken – I use it to create transparent shadows on objects.
Lighten – I use it (rarely) to lighten the texture.
Other types of Blending Mode are used very rarely, more when experimenting. Here is an example of me using the Color Dodge Blending Mode.
This link can serve as a good example of using multiple layers of the Blending Modes in the layers that lie one on another (link).