Illustrator - Making A Basic Pattern, video

A video tutorial follows at the end of the text tutorial.

Using the shape tool draw a circle.

Select the layers you want to use in your pattern. Then go to Object --> Pattern --> Make

Now the pattern editing window will pop up. For a basic polka dot pattern, change the "tile type" to brick by row, and increase the padding around your circle by changing the width and height of the pattern area. When you're done click on "done" near the top.

Now back in my original artboard I will hide the circle I made and draw a square the size of my canvas.

On the swatches panel (Window --> Swatches) you will see that your pattern has been saved. With your new square highlighted, set the fill to the polka dot pattern.

To change the size of your pattern, right click on the square and navigate to Transform -->Scale

In the window set the percent you want to shrink the pattern. Also, uncheck "transform object." Now you have a smaller pattern!