Follow these steps:
1. To begin with you need a shape or an art work that you want to use as a scatter brush. You can choose to use an existing object or create your own. I have created few rings (see below) which I would use as a scatter brush in this tutorial.

2. Select the entire art work and drag-drop into the Brushes panel. (To open the Brushes panel, go to Window > Brushes or find it on the panels list on the extreme right of your Illustrator workspace).
The ‘New Brush’ dialog box is prompted. Choose ‘Scatter Brush’ option and click OK. See below:

3. The Scatter Brush Options dialog appears next. Enter a name for the brush.

The sliders for Size, Spacing, Scatter and Rotation help you to determine how the pattern would be applied to the paths. Size: defines the size of the pattern in relation to the size of the original drawing.
Spacing: controls the distance between instances of the pattern.
Scatter: defines how apart the scatter brush pattern will be scattered.
Rotation: defines how much the pattern should rotate when applied to a curved path.
Colorization: defines how coloring should be added/not added to the original stroke color. Click on the Tips button to preview.

Adjust the sliders and click OK to exit from this dialog box.

NOTE: You can set all your sliders to ‘Random’ value (from the drop down). As soon as you choose a random value, another black slider appears that controls how much randomness to generate.

4. Now that your scatter brush is ready, apply it to a path using either of these ways:
a. Draw a path, choose the brush from the Brushes panel and the brush would be applied to selected the path.

b. Choose the scatter brush from the Brushes panel and then draw the path.

I created an ellipse and applied the scatter brush we just created.

If not happy with the results, double click on the Scatter brush (Scattered Rings) from the Brushes panel to open the ‘Scatter Brush Options’ dialog box and adjust the sliders.