A very simple, inexpensive way to start out teaching young children patterns would be to have three different colors of caps from gallon containers of milk or water.  Have several of each color.  If you don’t have the caps, then cut squares out of colored cardboard or paper.  Start with a very simple pattern and then make it progressively harder.  Start out demonstrating the whole pattern at first, showing how to duplicate the pattern to make sure the child understands the concept of “pattern.”  Then see if the child can duplicate it.  For example:

• Red, blue, red, blue, red, blue, ____, ____, ____, ____, ____, ____
• Red, green, red, green, red, green, ____, ____, ____, ____, ____
• Red, blue, blue, red, blue, blue, ____, ____, ____, ____, ____, ____
• Red, red, blue, red, red, blue, ____, ____, ____, ____, ____, ____
• Red, blue, green, red, blue, green, ____, ____, ____, ____, ____
• Red, green, green, blue, red, green, green, blue, ____, ____, ____, ____, ____, ____, ____, ____

As the child masters each level, have more complicated patterns.

Then add in two dimensions of color and shape:

• red circle, blue square, red circle, blue square
• red circle, green square, blue triangle, red circle, green square, blue triangle

As the child progresses, make patterns out of stickers (excellent way to make patterns) and other things besides color and shapes. Or you can use game pieces if you have multiple pieces that are the same. You could even use cans of green beans, corn, and tomatoes. Be creative with things around your house.